The Length Of The Subnormal To The Parabola y2 = 4ax at Any Point Is Equal To

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 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

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

The locus of a point whose some of the distance from the origin and the line x = 2 is 4 units, is

The slope of the normal at the point (at², 2at) of parabola y² = 4ax  is