1
If the ellipse x²/4 + y² = 1 meets the ellipse x² + y²/a^2 = 1 in four ...
Ellipse
2
P and Q are the foci of the ellipse x²/a^2 + y²/b^2 = 1 and B is an en ...
Ellipse
3
If the eccentricity of the ellipse x²/(a^2+1)+ y²/(a^2+2) = 1 is 1/√6, ...
Ellipse
4
An ellipse having foci at (3, 3) and (-4, 4) and passing through the o ...
Ellipse
5
A line of fixed length A+B moves so that its ends are always on two fi ...
Ellipse
6
A circle has the same centre as an ellipse and passes through the foci ...
Ellipse
7
The auxiliary circle of a family of ellipses passes through origin and ...
Ellipse
8
Let S and S' be two foci of the ellipse x²/a² + y²/b² = 1. If a circle ...
Ellipse
9
The sum of the squares of the perpendiculars on any two tangents to th ...
Ellipse
10
A tangent to the ellipse x²/a² + y²/b² = 1 at any point P meets the li ...
Ellipse
11
For the ellipse x²/9 + y²/4 = 1 with vertices A and A', tangent drawn ...
Ellipse
12
If a tangent of slope 2 of the ellipse x²/a² + y²/b² = 1 is normal to ...
Ellipse
13
An ellipse has the points (1,-1) and (2,-1) as its foci and x+y-5=0 as ...
Ellipse
14
If PQR is an equilateral triangle inscribed in the auxiliary circle of ...
Ellipse
15
Angle subtended by common tangents of two ellipses 4(x-4)² + 25y² = 10 ...
Ellipse
16
The eccentricity of locus of point (3h+2, k) where (h, k) lies on the ...
Ellipse
17
Locus of the point which divides double ordinates of the ellipse x²/a² ...
Ellipse
18
If the tangents to the ellipse x²/a² + y²/b² = 1 make angles α and β w ...
Ellipse
19
The locus of the point of intersection of tangents to an ellipse at tw ...
Ellipse
20
S₁ and S₂ are foci of an ellipse with a major axis of length 10 units ...
Ellipse
21
With a given point and line as focus and directrix, a series of ellips ...
Ellipse
22
The length of the major axis of the ellipse (5x-10)² + (5y +15)² = (3x ...
Ellipse
23
The line x = ^2r meets the ellipse x² + y²/9^2 = 1 in real and distinc ...
Ellipse
24
A man running round a race course notes that the sum of the distances ...
Ellipse
25
If the curves x²/4 + y² = 1 and x²/a^2 + y² = 1 for suitable value of ...
Ellipse
26
From any point P lying in first quadrant on the ellipse x²/25 + y²/16 ...
Ellipse
27
Let d₁ and d₂ be the lengths of the perpendiculars drawn from foci S a ...
Ellipse
28
A tangent having slope -4/3 to the ellipse x²/18 + y²/32 = 1 intersect ...
Ellipse
29
Let P be any point on a directrix of an ellipse of eccentricity e. S b ...
Ellipse
30
If(root3)bx + ay = 2ab touches the ellipse x²/a² + y²/b² = 1, then th ...
Ellipse
31
Number of distinct normal lines that can be drawn to the ellipse (x^2/ ...
Ellipse
32
If tangents PQ and PR are drawn from a point on the circle (x^2 + y^2 ...
Ellipse
33
There are exactly two points on the ellipse x²/a² + y²/b² = 1 whose di ...
Ellipse
34
The eccentric angle of a point on the ellipse x²/4 + y²/3 = 1 at a dis ...
Ellipse
35
The slopes of the common tangents of the ellipse and the circle (x^2/4 ...
Ellipse
36
The point of intersection of the tangents at the point P on the ellips ...
Ellipse
37
Ifα -β = a constant, then the locus of the point of intersection of ta ...
Ellipse
38
The normal at a variable point P on the ellipse x²/a² + y²/b² = 1 of e ...
Ellipse
39
Any ordinate MP of the ellipse x^2/25 + y^2/9 = 1 meets the auxiliary ...
Ellipse
