If `F_1` and `F_2` are the feet of the perpendiculars from the foci `S_1a n dS_2` of the ellipse `(x^2)/(25)+(y^2)/(16)=1` on the tangent at any point `P` on the ellipse, then prove that `S_1F_1+S_2F_2geq8.`

Let d_1a n dd_2 be the length of the perpendiculars drawn from the foci Sa n dS ' of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 to the tangent at any point P on the ellipse. Then, S P : S^(prime)P= (a) d_1: d_2 (b) d_2: d_1 (c) d_1 ^2:d_2 ^2 (d) sqrt(d_1):sqrt(d_2)

Two perpendicular tangents drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 intersect on the curve.

Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1.

The auxiliary circle of the ellipse x^(2)/25 + y^(2)/16 = 1

The foci of the ellipse 25(x + 1)^2 + 9(y + 2)^2 = 225

Locus of the feet of the perpendiculars drawn from either foci on a variable tangent to the hyperbola 16y^2 -9 x^2 = 1 is

Let d be the perpendicular distance from the centre of the ellipse x^2/a^2+y^2/b^2=1 to the tangent drawn at a point P on the ellipse. If F_1 & F_2 are the two foci of the ellipse, then show the (PF_1-PF_2)^2=4a^2[1-b^2/d^2] .

Tangents are drawn from any point on the circle x^(2)+y^(2) = 41 to the ellipse (x^(2))/(25)+(y^(2))/(16) =1 then the angle between the two tangents is

The maximum distance of the centre of the ellipse (x^(2))/(16) +(y^(2))/(9) =1 from the chord of contact of mutually perpendicular tangents of the ellipse is

Tangents are drawn from the point P(3, 4) to the ellipse x^2/9+y^2/4=1 touching the ellipse at points A and B.