1
P and Q are the foci of the ellipse x²/a^2 + y²/b^2 = 1 and B is an end of the minor axis. If PBQ is ...
2
An ellipse having foci at (3, 3) and (-4, 4) and passing through the origin has eccentricity equal t ...
3
If the eccentricity of the ellipse x²/(a^2+1)+ y²/(a^2+2) = 1 is 1/√6, then latus rectum of ellipse ...
4
If PQR is an equilateral triangle inscribed in the auxiliary circle of the ellipse x²/a² + y²/b² = 1 ...
5
S₁ and S₂ are foci of an ellipse with a major axis of length 10 units and P is any point on the elli ...
6
If the ellipse x²/4 + y² = 1 meets the ellipse x² + y²/a^2 = 1 in four distinct points and a = b² - ...
7
With a given point and line as focus and directrix, a series of ellipses are described, the locus of ...
8
A line of fixed length A+B moves so that its ends are always on two fixed perpendicular straight lin ...
9
The length of the major axis of the ellipse (5x-10)² + (5y +15)² = (3x-4y+7)²/4 is ...
10
Angle subtended by common tangents of two ellipses 4(x-4)² + 25y² = 100 and 4(x+1)² + y² = 4 at orig ...
11
A circle has the same centre as an ellipse and passes through the foci F₁ and F₂ of the ellipse, suc ...
12
The line x = ^2r meets the ellipse x² + y²/9^2 = 1 in real and distinct points if and only if ...
13
The auxiliary circle of a family of ellipses passes through origin and makes intercepts of 8 and 6 u ...
14
A man running round a race course notes that the sum of the distances of two flagposts from him is a ...
15
There are exactly two points on the ellipse x²/a² + y²/b² = 1 whose distance from its centre is the ...
16
The eccentricity of locus of point (3h+2, k) where (h, k) lies on the circle x² + y² = 1 is ...
17
Let S and S' be two foci of the ellipse x²/a² + y²/b² = 1. If a circle described on SS' as diameter ...
18
The eccentric angle of a point on the ellipse x²/4 + y²/3 = 1 at a distance of 5/4 units from the fo ...
19
If the curves x²/4 + y² = 1 and x²/a^2 + y² = 1 for suitable value of a cut on four concyclic points ...
20
From any point P lying in first quadrant on the ellipse x²/25 + y²/16 = 1, PN is drawn perpendicular ...
21
Let d₁ and d₂ be the lengths of the perpendiculars drawn from foci S and S' of the ellipse x²/a² + y ...
22
Locus of the point which divides double ordinates of the ellipse x²/a² + y²/b² = 1 in the ratio 1:2 ...
23
The sum of the squares of the perpendiculars on any two tangents to the ellipse x²/a² + y²/b² = 1 fr ...
24
The slopes of the common tangents of the ellipse and the circle (x^2/4 + y^2/1 = 1) , x^2+y^2 =3 a ...
25
The point of intersection of the tangents at the point P on the ellipse x²/a² + y²/b² = 1 the auxili ...
26
If the tangents to the ellipse x²/a² + y²/b² = 1 make angles α and β with the major axis such that t ...
27
A tangent to the ellipse x²/a² + y²/b² = 1 at any point P meets the line x = 0 at a point Q. Let R b ...
28
For the ellipse x²/9 + y²/4 = 1 with vertices A and A', tangent drawn at the point P in the first qu ...
29
A tangent having slope -4/3 to the ellipse x²/18 + y²/32 = 1 intersects the major and minor axes at ...
30
Let P be any point on a directrix of an ellipse of eccentricity e. S be the corresponding focus and ...
31
If a tangent of slope 2 of the ellipse x²/a² + y²/b² = 1 is normal to the circle (x^2 + y^2 + 4x + 1 ...
32
Ifα -β = a constant, then the locus of the point of intersection of tangents at P (a cos α, b sin α) ...
33
The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentr ...
34
If(root3)bx + ay = 2ab touches the ellipse x²/a² + y²/b² = 1, then the eccentric angle of the point ...
35
The normal at a variable point P on the ellipse x²/a² + y²/b² = 1 of eccentricity e meets the axes o ...
36
Any ordinate MP of the ellipse x^2/25 + y^2/9 = 1 meets the auxiliary circle at Q, then the locus of ...
37
Number of distinct normal lines that can be drawn to the ellipse (x^2/169 + y^2/25 = 1) from the poi ...
38
An ellipse has the points (1,-1) and (2,-1) as its foci and x+y-5=0 as one of its tangents. Then the ...
39
If tangents PQ and PR are drawn from a point on the circle (x^2 + y^2 =25 ) to the ellipse (x^2/4 + ...
