The is a point P on the hyperbola `(x^(2))/(16)-(y^(2))/(9)=1` such that its distance from the right directrix is the average of its distance from the two foci. Then the x-coordinate of P is (a)`-64/5` (b)`-32/9` (c)`-64/9` (d)none of these

Options

A. `-64//5`
B. `-32//9`
C. `-64//9`
D. none of these

Answer

A

Explanation

Let `P-=(x,y)`
`therefore" "(a)/(e)+x=((ex-a)+(ex+a))/(2)`
`therefore" "(a)/(e)+x=ex`
`therefore" "(16)/(5)+x=(5)/(4)x`
`x=(64)/(5)`
But, point P lies on the left branch.
Therefore, x-coordinate of P is `(-64)/(5)`.