If `S_1 and S_2` are the foci of the ellipse `x^2/8^2 + y^2/3^2 =1` and length of perpendicular from centre to tangent drawn at a point `P` on the ellipse be 4, then `(PS_1 - PS_2)^2 =`

Let P be a point on the ellipse x^2/100 + y^2/25 =1 and the length of perpendicular from centre of the ellipse to the tangent to ellipse at P be 5sqrt(2) and F_1 and F_2 be the foci of the ellipse, then PF_1.PF_2 .

Product of perpendiculars drawn from the foci upon any tangent to the ellipse 3x^(2)+4y^(2)=12 is

If p is the length of the perpendicular from the focus S of the ellipse x^(2)/a^(2)+y^(2)/b^(2) = 1 to a tangent at a point P on the ellipse, then (2a)/(SP)-1=

If M_(1) and M_(2) are the feet of perpendiculars from foci F_(1) and F_(2) of the ellipse (x^(2))/(64)+(y^(2))/(25)=1 on the tangent at any point P of the ellipse then

The product of the perpendiculars from the two foci of the ellipse (x^(2))/(9)+(y^(2))/(25)=1 on the tangent at any point on the ellipse

Number of points on the ellipse (x^(2))/(25) + (y^(2))/(16) =1 from which pair of perpendicular tangents are drawn to the ellipse (x^(2))/(16) + (y^(2))/(9) =1 is

Angle between the tangents drawn from point (4, 5) to the ellipse x^2/16 +y^2/25 =1 is