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The equation of a tangent to the parabol...

The equation of a tangent to the parabola `y^(2)=8x` which makes an angle `45^(@)` with the line y = 3x + 5 is

A

`x+2y+1=0`

B

`2x+y +1=0`

C

`x+y +2=0`

D

`x+y +1=0`

Text Solution

Verified by Experts

The correct Answer is:
B

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`
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