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Question

The equation of a tangent to the parabola y2=8x which makes an angle 45 with the line y=3x+5 is

A
2x+y+1=0
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B
y=2x+1
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C
x+2y+8=0
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D
x2y+8=0
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Solution

The correct option is D x2y+8=0
Equation of tangent in term of slope of
y2=8x is
y=mx+2m(i)
Angle between (i) and y=3x+5 is 45, then
m31+3m=tan45=1±(m3)=1+3m

When m3=1+3m
m=2
When m+3=1+3m
m=12

Now, the equation of tangents are
y=2x1 and y=x2+42x+y+1=0 and x2y+8=0

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