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

Step-by-step solution

Given equation of ellipse is x^2 9 + y^2 25 =1 , Here b a aligned & c^2=b^2-a^2=25-9=16 c= 4 & foci =(0, 4) aligned Let the tangent be y=m x+C where C^2=a^2 m^2+b^2 C^2=9 m^2+25 ...(i) Product of distance from focii to tangent = ( 0-4+C 1+m^2 ) ( 0+4+C 1+m^2 )= C^2-16 1+m^2 = 9 m^2+25-16 1+m^2 =9