Ellipse questions
211 published questions with worked solutions.
- For some (0, 2 ), if the eccentricity of the hyperbola, x^2-y^2 ^2 =10 is 5 times the eccentricity of the ellipse, x^2 ^2 +y^2=5,...
- Let x^2 a^2 + y^2 b^2 =1 (a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value...
- Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 1 2 . If P(1, ), > 0 is a point on...
- Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, x^2 4 + y^2 2...
- If a>0 and the equation |z-a^2 |+|z-2a|=3 represents an ellipse, then a belongs to the interval
- Let A be the point (3, 0) and circles with variable diameter AB touch the circle x² + y² = 36 internally. Let the curve C be the...
- Let an ellipse x^2 a^2 + y^2 b^2 = 1, a < b, pass through the point (4, 3) and have eccentricity 5 3 . Then the length of its...
- Consider the parabola P : y² = 4kx and the ellipse E : x^2 a^2 + y^2 b^2 =1. Let the line segment joining the points of...
- Let a focus of the ellipse E : x²/a²+y²/b²=1 be S(4,0) and its eccentricity be 4/5. If the point P(3,α) lies on E and O is the...
- Let x=9 be a directrix of an ellipse E, whose centre is at the origin and eccentricity is 1/3. Let P(α,0), α>0, be a focus of E...
- Let x^2 f(a^2+7a+3) + y^2 f(3a+15) =1 represent an ellipse with major axis along y-axis, where f is a strictly decreasing...
- Let f(x) = x² + 9, g(x) = x/(x − 9) and a = fog(10), b = gof(3). If e and ℓ denote the eccentricity and the length of the latus...
- The length of the chord of the ellipse x^2 25 + y^2 16 = 1, whose mid point is (1, 25 ), is equal to :
- Let A(α, 0) and B(0, β) be the points on the line 5x + 7y = 50. Let the point P divide the line segment AB internally in the...
- If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the...
- If the point of intersections of the ellipse x^2 16 + y^2 b^2 =1 and the circle x^2+y^2=4b, b > 4 lie on the curve y^2=3x^2, then...
- Let a tangent be drawn to the ellipse x^2 27 +y^2=1 at (3 3 , ) where (0, 2 ). Then the value of such that the sum of intercepts...
- Let E_1: x^2 a^2 + y^2 b^2 =1, a > b. Let E_2 be another ellipse such that it touches the end points of major axis of E_1 and the...
- Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3, –4), one focus at (4, –4) and one...
- If the minimum area of the triangle formed by a tangent to the ellipse x^2 b^2 + y^2 4a^2 =1 and the co–ordinate axis is kab,...
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