Ellipse Test - ...

Q is a point on the auxiliary circle corresponding to the point P of the ellipse  If T is the foot of the perpendicular dropped from the focus S on to the tangent to the auxiliary circle at Q then the ΔSPT is :

Let x and y satisfy the relation x² + 9y² - 4x + 6y + 4 = 0, then maximum value of the expression (4x - 9y),

A rectangle ABCD has area 200 square units. An ellipse with area 200π passes through A and C and has foci at B and D, then

A tangent to the ellipse  at any point P meet the line x = 0 at a point Q. Let R be the image of Q in the line y = x, then circle whose extremities of a diameter are Q and R passes through a fixed point. The fixed point is

If the curve x² + 3y² = 9 subtends an obtuse angle at the point (2α, α), then a possible value of α² is 

Let S = 0 be the equation of reflection of  about the line x – y – 2 = 0. Then the locus of point of intersection of perpendicular tangents of S is

Any ordinate MP of a ellipse  meets the auxiliary circle in Q, then locus of point of intersection of normals at P and Q to the respective curves, is

The radius of the largest circle whose centre at (-3,0) and is inscribed in the ellipse 16x² + 25y² = 400 is

The line passing through the extremely A of the major axis and extremity B of the minor axis of the ellipse x² + 9y² = 9 meets its auxiliary circle at the point M . Then the area of the triangle with vertices at A,M and the origin O is

Coordinate of the vertices B and C of triangle ABC are respectively (2, 0) and (8, 0). The vertex ‘A’ is varying in such a way that  Then the locus of ‘A’ is an ellipse whose major axis is of length.