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

On which curve does the perpendicular tangents drawn to the hyperbola (x^2)/(25)-(y^2)/(16)=1 intersect?

Statement 1 : There can be maximum two points on the line p x+q y+r=0 , from which perpendicular tangents can be drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 Statement 2 : Circle x^2+y^2=a^2+b^2 and the given line can intersect at maximum two distinct points.

The number of points on the ellipse (x^2)/(50)+(y^2)/(20)=1 from which a pair of perpendicular tangents is drawn to the ellipse (x^2)/(16)+(y^2)/9=1 is (a)0 (b) 2 (c) 1 (d) 4

Prove that the chords of constant of perpendicular tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touch another fixed ellipse (x^(2))/(a^(4))+(y^(2))/(b^(4))=(1)/((a^(2)+b^(2)))

The points on the ellipse (x^(2))/(2)+(y^(2))/(10)=1 from which perpendicular tangents can be drawn to the hyperbola (x^(2))/(5)-(y^(2))/(1) =1 is/are

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.

Prove that the chords of contact of pairs of perpendicular tangents to the ellipse x^2/a^2+y^2/b^2=1 touch another fixed ellipse.

The locus of the point of intersection of perpendicular tangents to the hyperbola (x^(2))/(25)-(y^(2))/(9) is:

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

If from a point P(0, alpha ) , two normals other than the axes are drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 , such that | alpha | < k , then the value of 4k is______