Let `x^2/a^2+y^2/b^2=1 and x^2/A^2-y^2/B^2=1` be confocal `(a > A and a> b)` having the foci at `s_1 and S_2,` respectively. If P is their point of intersection, then `S_1 P and S_2 P` are the roots of quadratic equation

Options

A. `x^(2)+2ax+(a^(2)-A^(2))=0`
B. `x^(2)+2ax+(a^(2)-A^(2))=0`
C. `x^(2)-2Ax+(a^(2)+A^(2))=0`
D. `x^(2)-2ax+(a^(2)-A^(2))=0`

Answer

D

Explanation

`S_(1)+S_(2)P=2a and S_(1)P-S_(2)P=2A`
`S_(1)+=a+A and S_(2)P=(a-A)`
Required quadratic equation is `x^(2)-2ax+(a^(2)-A^(2))=0`