If line `P Q` , where equation is `y=2x+k` , is a normal to the parabola whose vertex is `(-2,3)` and the axis parallel to the x-axis with latus rectum equal to 2, then the value of `k` is `(58)/8` (b) `(50)/8` (c) `1` (d) `-1`

Options

A. `58//8`
B. `50//8`
C. 1
D. `-1`

Answer

C

Explanation

(3) `4a=2ora=(1)/(2)`
Vertex `-=(-2,3)`
So, the parabola is
`(y-3)^(2)=2(x+2)`
The equation of normal to the parabola is
`(y-3)=m(x+2)-m-(1)/(2)m^(3)`
`ory=mx+m+3-(1)/(2)m^(3)`
Also, given y=2x+k. Here, m=2.
`k=m+3-(1)/(2)m^(3)`
`=2+3-(1)/(2)(2)^(3)=5-4=1`