If the tangent at point P(h, k) on the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` cuts the circle `x^(2)+y^(2)=a^(2)` at points `Q(x_(1),y_(1))` and `R(x_(2),y_(2))`, then the vlaue of `(1)/(y_(1))+(1)/(y_(2))` is

Options

A. a. 3
B. `-3`
C. `4`
D. `-4`

Answer

D

Explanation

Line `L:(x+7)/(a)=(y-y_(1))/(-b)=(z-z_(1))/(c)`
`(-7,y,z_(1))` lie on plane `P_(1)`
`implies-3y_(1)+z_(1)=9` ,…(1)
Line L lies on plate `P_(2)`
`impliesa+4b+14c=0` ..(2)
Also `(-7,y_(1),z_(1))` lies on `P_(2)`
`implies-4y_(1)-14z_(1)=12` .. (3)
Form (1) and (3)
Line passes through `(-7,-3,0)`
Least value of a,b,c is `a=2,b=3,c=1`
(from (2))