Ellipse Test - ...

If maximum distance of any point on the ellipse x² + 2y² + 2xy = 1 from its centre be r, then r is equal to 

The equation of the line passing through the centre and bisecting the chord 7x +y -1 = 0 of the ellipse 

Eccentricity of ellipse  such that the line joining the foci subtends a right angle only at two points on ellipse, is

The tangent at the point ‘a’ on the ellipse  meets the auxiliary circle in two points which subtends a right angle at the centre, then the eccentricity ‘e’ of the ellipse is given by the equation :

The number of values of c such that the straight line y = 4x+ c touches the curve 

If tangents are drawn to the ellipse x² + 2y² = 2, then the locus of the midpoint of the intercept made by the tangent between the coordinate axes is

An ellipse with major and minor axes, 6√3 and 6 respectively slides along the coordinate axes and always remains confined in the first quadrant. If the length of arc described by the centre of the ellipse is then the value of k is

Consider the ellipse  and the parabola y² = 2x. They intersect at P and Q in the first and fourth quadrants respectively. Tangents to the ellipse at P and Q intersect the x-axis at R and tangents to the parabola at P and Q intersect the x-axis at S. If the area of quadrilateral PQRS, is λ then 

The area of the quadrilateral formed by the tangents at the end points of latus rectum of the ellipse  is k then k/9 is

The length of the focal chord of the ellipse  which is inclined to x – axis at an angle 45° is λ, then