Question

The maximum distance of the centre of the ellipse from the chord of contact of mutually perpendicular tangents of the ellipse is




1)




12/5 




2)




4/5   




3)




32/5    




4)




16/5

Answer 1

ФФThe maximum distance of the centre of the ellipse from the chord of contact of mutually perpendicular tangents of the ellipse is

Answer:

16/5

Step-by-step explanation:

Perpendicular tangents meet on director circle  x²+ y² =25

Equation of chord of contact of ellipse w.r.t this point is

5cosФ x/ 16 + 5sinФy/9 = 1

Distance from center    = 1/√{25/256cos^{2} Ф +√25/81sin^{2}Ф

Maximum value cosФ = 1 and sin Ф = 0

Therefore the maximum distance is 16/5