A tangent to the parabola `y^(2) = 8x` makes an angle of `45^(@)` with the straight line `y = 3x + 5`. Find its equation and its point of contact.

Options

A. `x+2y+1=0`
B. `2x+y +1=0`
C. `x+y +2=0`
D. `x+y +1=0`

Answer

B

Explanation

Equation of any tangent to the parabola `y^(2)=8x` is `y=mx +(a)/(m)=mx +(2)/(m)`
`L: y=3x+5`
`:.tan45^(@)=|(m-3)/(1+3m)|`
`rArr (m-3)/(1+3m)=pm1`
`rArr m-3=1+3m rArr m-3= -1-3m`
`rArr m-3m=4 rArr 4m=2 rArr m=(4)/(-2)= -2 rArr m=(1)/(2)`
Equation of tangent is `y= -2x-1`
`y=(1)/(2)x +4 rArr y+2x+1=0 rArr 2y-x-8=0`