Prove that the sum of the focal distance of any point on the ellipse is constant and is equal to the length of the major axis.

Find the sum of the focal distances of any point on the ellipse 9x^2+16 y^2=144.

show that the absolute value of the focal distances of any point P on the hyperbola in the length of its transverse axis.

The sum of distance of any point on the ellipse 3x^2 + 4y^2 = 24 from its foci is

Which of the following is/are true about the ellipse x^2+4y^2-2x-16 y+13=0? the latus rectum of the ellipse is 1. The distance between the foci of the ellipse is 4sqrt(3)dot The sum of the focal distances of a point P(x , y) on the ellipse is 4. Line y=3 meets the tangents drawn at the vertices of the ellipse at points P and Q . Then P Q subtends a right angle at any of its foci.

Focal length is equal to half of the

Let the length of latus rectum of an ellipse with its major axis along x-axis and center at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of the minor axis , then which of the following points lies on it: (a) (4sqrt2, 2sqrt2) (b) (4sqrt3, 2sqrt2) (c) (4sqrt3, 2sqrt3) (d) (4sqrt2, 2sqrt3)

Consider the ellipse E_1, x^2/a^2+y^2/b^2=1,(a>b) . An ellipse E_2 passes through the extremities of the major axis of E_1 and has its foci at the ends of its minor axis.Consider the following property:Sum of focal distances of any point on an ellipse is equal to its major axis. Equation of E_2 is

Prove that the locus of a point, which moves so that its distance from a fixed line is equal to the length of the tangent drawn from it to a given circle, is a parabola.

Sum of the focal distance of the ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 is

Prove that the focal distance of the point (x ,y) on the parabola x^2-8x+16 y=0 is |y+5|