In an ellipse, the sum of the distances between foci is always less than the sum of focal distances of any point on it. Statement 2 : The eccentricity of any ellipse is less than 1.

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

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

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.

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

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.

If the distance between the foci is 2 and the distance between the directrices is 5 , then the equation of the ellipse is

Find the sum of all odd integers less than 450.

If the tangent at any point of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosbeta/(cosalpha)