1.

A tangent to the parabola y^(2)=8x makes an angle of45^(@)with the straight liney=3x+5. The equation of tangent is:

Answer»

`x+2y+1=0`
`2x+y +1=0`
`x+y +2=0`
`x+y +1=0`

SOLUTION :
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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