The equation of the normal to the curve parametrically represented by `x=t^(2)+3t-8 and y=2t^(2)-2t-5` at the point `P(2,-1)` is

Options

A. `2x+3y-1=0`
B. `6x-7y-11=0`
C. `7x+6y-8=0`
D. `3x+y-1=0`

Answer

C

Explanation

`{:(t^(2)+3t-8=2 rArrt=2","-5),(2t^(2)-2t-5=-1 rArr t=2","-1):}}`
`rArr" "t=2,(dy)/(dx)=(4t-2)/(2t+3)rArr ((dy)/(dx))_(t=2)=(6)/(7)`
`therefore" Equation of normal y + 1"=(-7)/(6)(x-2)`