The Tangent At Any Point P of The Hyperbola  makes An Intercept Of Length p between The Point Of Contact And The Transverse Axis Of The Hyperbola, p1, p2 are The Lengths Of The Perpendiculars Drawn From The Foci On The Normal At P, Then

If F₁ = (3, 0), F₂ = (–3, 0) and P is any point on the curve 16x² +25y² = 400, then PF₁ + PF₂ equal

The locus of the points of intersection of the tangents at the extremities of the chords of the ellipse x² + 2y² = 6 which touch the ellipse x² + 4y² = 4 is

The normal at an end of a latus rectum of the ellipse  passes through an end of the minor axis if

If an ellipse slides between two perpendicular straight line, then the locus of its center is   

If the tangent at a point on the ellipse  meets the auxillary circle in two points, the chords joining them subtends a right angle at the center; then the eccentricity of the ellipse is given by

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

The normal at a point P on the ellipse x² + 4y² = 16 meets the x-axis at Q, then locus of M intersects the latus rectums of the given ellipse at the points.

Let a and b be non-zero real numbers. Then the equation (ax² + by² + c)(x² – 5xy + 6y²) = 0 represents

The pints of intersection of the two ellipse x² + 2y² – 6x – 12y + 23 = 0 and 4x² + 2y² – 20x – 12y + 35 = 0.

The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola y² = 8x, is