If `x+y=k` is normal to `y^2=12 x ,` then `k` is 3 (b) 9 (c) `-9` (d) `-3`

Options

A. 3
B. 9
C. -9
D. -3

Answer

B

Explanation

Let `x+y=k` be normal to
`y^(2)=12xx at p(alpha,beta)" "...(i)`
`thereforebeta^(2)=12 alpha" "...(ii)`
Also, slope of normal at `P(alpha, beta)` is -1 From, Eq. (i),
`(dy)/(dx)=6/y`
`implies((dy)/(dx))_(p)=(6)/(beta)`
`therefore -1 =(-1)/(6//beta)`
`impliesbeta=6,alpha =3`
`thereforeP` is (3,6) which lies on `x+y=k`
`therefore 3+6=k`
`impliesk=9`