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 the curve
`y^(2)=12x` at `P(alpha, beta)` …………….i
`:. beta^(2)=12alpha` ……………ii
Also, slope of normal at `P(alpha, beta)` is -1
From Eq. (i) `(dy)/(dx)=6/y`
At `P(alpha, beta)((dy)/(dx))_(p)=6/(beta),implies1=(-1)/(6//beta)`
`implies beta=6`, then from Eq. (ii) `alpha=3`
Also point `P(3,6)` lies on `x+y=k`
`:.3+6=kimpliesk=9`