Conic Sections — Class 11 solved problems

68 problems from this chapter, each solved step by step.

Find the equation of the circle passing through points (1,2), (3,4), and (5,2).
The equation of the circle is x² + y² - 6x - 4y + 9 = 0.
Determine the equation of the circle with radius 4 and Centre (-2, 3).
The equation of the circle is (x + 2)² + (y - 3)² = 16.
Find the equation of the hyperbola where foci are (0, +-6) and the length of the latus rectum is 36.
The equation of the hyperbola is y²198 - 54√13 - x²-162 + 54√13 = 1.
Find the equation of the hyperbola where foci are (0, ± 12) and the length of the latus rectum is 36
The equation of the hyperbola is (y²)/(36) - (x²)/(108) = 1.
Find the equation of the circle with centre (-3,2) and radius 10.
The equation of the circle is (x+3)² + (y-2)² = 100.
Find the equation of the circle with centre (-3,2) and radius 9.
(x+3)² + (y-2)² = 81
Find the equation of the circle with centre (-3,2) and radius 8.
The equation of the circle is (x + 3)² + (y - 2)² = 64
Find the equation of the circle with centre (-3,2) and radius 6.
The equation of the circle is (x+3)² + (y-2)² = 36.
Find the equation of the circle with centre (-3,8) and radius 7.
The equation of the circle is (x+3)² + (y-8)² = 49.
Find the equation of the circle with centre (-2,7) and radius 5.
The equation of the circle is (x+2)² + (y-7)² = 25.
Find the equation of the circle with centre (-5,4) and radius 6.
(x+5)² + (y-4)² = 36
Find the centre and the radius of the circle x²+y²+8 x+10 y-8=0.
The center of the circle is (-4, -5) and the radius is 7.
The length of the chord of the ellipse (x²)/(4) + (y²)/(2) = 1, whose mid-point is (1, (1)/(2)), is:
The length of the chord is √((11)/(3)).
Let for two distinct values of p the lines y = x + p touch the ellipse E: (x²)/(4)+(y²)/(3)=1 at the points A and B. Let the line y = x intersect E at the point
(20√6)/(7)
A rod of length eight units moves such that its ends A and B always lie on the lines x-y+2=0 and y+2=0, respectively. If the locus of the point P, that divides
23
Find the equation of the tangent to the ellipse x²/16 + y²/9 = 1 that passes through the point (8, 0).
The equations of the tangents are y = (√3)/(4)x - 2√3 and y = -(√3)/(4)x + 2√3.
Find an equation of the circle with centre at (0,0) and radius r.
The equation of the circle with centre at (0,0) and radius r is x² + y² = r².
A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point (2, 5) and
15
Find the equation of the hyperbola with foci (0, ± 3) and vertices (0, ± (√11)/(2)).
The equation of the hyperbola is (4y²)/(11) - (4x²)/(25) = 1.
Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b, respectively, and one focus and the corresponding directrix o
(152109)/(850)
Let E: (x²)/(a²) + (y²)/(b²) = 1, a > b and H: (x²)/(A²) - (y²)/(B²) = 1. Let the distance between the foci of E and the foci of H be 2√3. If a - A = 2, and the
8
If the equation of the parabola with vertex V((3)/(2), 3) and the directrix x + 2y = 0 is α x² + β y² - xy - 30x - 60y + 225 = 0, then α + β + is equal to:
9
MODIFIED: Find the equation of the tangent to the ellipse variable_97²/16 + variable_97²/9 = 1 that passes through the point (8, 0).
The equations of the tangents are y = (√3)/(4)x - 2√3 and y = -(√3)/(4)x + 2√3.
Find the equation of the circle which passes through the points (2,-2), and (3,4) and whose centre lies on the line x+y=2.
The equation of the circle is (x-(7)/(10))² + (y-(13)/(10))² = (629)/(50).
Let E_1: (x²)/(5) + (y²)/(4) = 1 be an ellipse. Ellipses E_i are constructed such that their centres and eccentricities are same as that of E_1, and the length
50√5
Let the focal chord PQ of the parabola y² = 4x make an angle of 60^° with the positive x-axis, where P lies in the first quadrant. If the circle, whose one diam
15
Find the equation of the ellipse, whose length of the major axis is 20 and foci are (0, ± 5).
The equation of the ellipse is (x²)/(75) + (y²)/(100) = 1.
Let P be the parabola, whose focus is (-2, 1) and directrix is 2x + y + 2 = 0. Then the sum of the ordinates of the points on P, whose abscissa is -2, is:
The sum of the ordinates of the points on P, whose abscissa is -2, is (3)/(2).
If the equation of the hyperbola with foci (4,2) and (8,2) is 3x² - y² - ax + by + = 0, then a + b + is equal to:
132
Let the parabola y = x² + p x - 3 meet the coordinate axes at the points P, Q, and R. If the circle C with centre at (-1, -1) passes through the points P, Q, an
6 square units
Let C be the circle x² + (y-1)² = 2, E_1 and E_2 be two ellipses whose centres lie at the origin and major axes lie on the x-axis and y-axis respectively. Let t
46
If the four distinct points (4,6), (-1,5), (0,0) and (k,3k) lie on a circle of radius r, then 10k + r² is equal to:
35
Let ABCD be a trapezium whose vertices lie on the parabola y² = 4x. Let the sides AD and BC of the trapezium be parallel to y -axis. If the diagonal AC is of le
(49)/(4)
If the line 3x - 2y + 12 = 0 intersects the parabola 4y = 3x² at the points A and B, then at the vertex of the parabola, the line segment AB subtends an angle e
The angle subtended by the line segment AB at the vertex of the parabola is tan^(-1)((9)/(7)).
Find the coordinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas: (i) (x²)/(9)-(y²)/(16)=1, (ii) y²-16 x²=1
(i) Foci: (± 5, 0), Vertices: (± 3, 0), Eccentricity: (5)/(3), Length of latus rectum: (32)/(3). (ii) Foci: (0, ± √17), Vertices: (0, ± 4), Eccentricity: (√17)/
Find the equation of the ellipse, with major axis along the x -axis and passing through the points (4,3) and (-1,4).
7x² + 15y² = 247
Let the ellipse E_1: (x²)/(a²) + (y²)/(b²) = 1, a > b and E_2: (x²)/(A²) + (y²)/(B²) = 1, A < B have the same eccentricity (1)/(√3). Let the product of their le
The area of the quadrilateral ABCD is (24√6)/(5).
If α x+β y=109 is the equation of the chord of the ellipse (x²)/(9)+(y²)/(4)=1, whose midpoint is ((5)/(2), (1)/(2)), then α+β is equal to:
58
Let circle C be the image of x² + y² - 2x + 4y - 4 = 0 in the line 2x - 3y + 5 = 0 and A be the point on C such that OA is parallel to x -axis and A lies on the
4
Let C_1 be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let C_2 be the circle with centre (1, 3) that touches C_1 externally
22
Let H_1: (x²)/(a²) - (y²)/(b²) = 1 and H_2: -(x²)/(A²) + (y²)/(B²) = 1 be two hyperbolas having length of latus rectums 15 √2 and 12 √5 respectively. Let their
55
Let the product of the focal distances of the point (√3, (1)/(2)) on the ellipse (x²)/(a²) + (y²)/(b²) = 1, (a > b), be (7)/(4). Then the absolute difference of
(3√3 - 2√6)/(6)
The length of the latus-rectum of the ellipse whose foci are (2,5) and (2,-3) and eccentricity is (4)/(5) is:
(18)/(5)
Find the equation of the parabola with vertex at (0,0) and focus at (0,2).
The equation of the parabola is x² = 8y.
Let the shortest distance from (a, 0), a > 0, to the parabola y² = 4x be 4. Then the equation of the circle passing through the point (a, 0) and the focus of th
(x-3)² + y² = 4
If S and S' are the foci of the ellipse (x²)/(18) + (y²)/(9) = 1 and P is a point on the ellipse, then min (SP· S'P) + max (SP· S'P) is equal to:
27
Find the equation of the parabola which is symmetric about the y -axis, and passes through the point (2,-3).
The equation of the parabola is x² = -(4)/(3)y.
The focus of the parabola y² = 4x + 16 is the centre of the circle C of radius 5. If the values of, for which C passes through the point of intersection of the
15
Let the equation of the circle, which touches x -axis at the point (a, 0), a > 0 and cuts off an intercept of length b on y -axis be x² + y² - α x + β y + = 0.
(2a, 4r² - 4a²)
Let C be the circle of minimum area enclosing the ellipse (x²)/(a²)+(y²)/(b²)=1 with eccentricity 12 and foci ( 2,0). Let PQR be a variable triangle whose verte
29(2 + √3)
The equation of the chord of the ellipse (x²)/(25) + (y²)/(16) = 1, whose mid-point is (3, 1), is:
The equation of the chord is 48x + 25y - 169 = 0.
Let y² = 12x be the parabola and S be its focus. Let PQ be a focal chord of the parabola such that (SP)(SQ) = (147)/(4). Let C be the circle described taking PQ
1328
Let A = (α, β) R × R: |α - 1| ≤ 4 and |β - 5| ≤ 6 and B = (α, β) R × R: 16(α - 2)² + 9(β - 6)² ≤ 144. Then:
B is a subset of A.
Let r be the radius of the circle, which touches the x-axis at point (a, 0), a < 0 and the parabola y² = 9x at the point (4, 6). Then r is equal to _____
30
A line passing through the point P(√5,√5) intersects the ellipse (x²)/(36)+(y²)/(25)=1 at points A and B such that (PA)·(PB) is maximum. Then 5 (PA²+PB²) is equ
(119)/(18)
Let one focus of the hyperbola H:(x²)/(a²)-(y²)/(b²)=1 be at (√10,0) and the corresponding directrix be x=(9)/(√10). If e and l respectively are the eccentricit
16
Let the line x + y = 1 meet the circle x² + y² = 4 at the points A and B. If the line perpendicular to AB and passing through the midpoint of the chord AB inter
2√14
The absolute difference between the squares of the radii of the two circles passing through the point (-9,4) and touching the lines x+y=3 and x-y=3 is equal to:
768
Let the foci of a hyperbola be (1, 14) and (1, -12). If it passes through the point (1, 6), then the length of its latus-rectum is:
The length of the latus-rectum is (288)/(5).
Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9 x²+4 y²=36.
The coordinates of the foci are (0, ± √5). The coordinates of the vertices are (0, ± 3). The length of the major axis is 6 units. The length of the minor axis i
If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is:
The eccentricity of the ellipse is (4√17)/(17).
The centre of a circle C is at the centre of the ellipse E: (x²)/(a²)+(y²)/(b²)=1, a>b. Let C pass through the foci F_1 and F_2 of E such that the circle C and
13
The shortest distance between the curves y² = 8x and x² + y² + 12y + 35 = 0 is:
2√2 - 1
Find the equation of the ellipse whose vertices are ( ± 13,0) and foci are ( ± 5,0).
The equation of the ellipse is (x²)/(169) + (y²)/(144) = 1.
Let the circle C touch the line x - y + 1 = 0, have the centre on the positive x -axis, and cut off a chord of length (4)/(√13) along the line -3x + 2y = 1. Let
16 + 12√2
Let the length of a latus rectum of an ellipse (x²)/(a²) + (y²)/(b²) = 1 be 10. If its eccentricity is the minimum value of the function f(t) = t² + t + (11)/(1
126
Consider the hyperbola (x²)/(a²) - (y²)/(b²) = 1 having one of its foci at P = (-3, 0). If the latus rectum through its other focus subtends a right angle at P
α = 810, β = 1134
Find the equation of the circle with centre (-3,2) and radius 4.
(x+3)² + (y-2)² = 16

More Class 11 chapters

Solve your own maths question free →