A tangent to the parabola lsquo y2 8x rsquo makes an angle of 45 deg with the straight line y 4x 5 F...........

Mathematics (NDA) Coordinate Geometry

A tangent to the parabola ‘y² = 8x’ makes an angle of 45° with the straight line y = 4x + 5. Find its equation and its point of contact?

y=-3x +10/3

5y=3x +10

5y=3x +10/3

5y=x +10/3

Let the slope of tangent be m

Line y = 4x + 5

m=4

parabola y² = 8x ,a=2

tan 45 °=±(4-m/1+4m)

1=4-m/1+4m (positive)

1+4m =4-m

m=3/5

1 =-4+m/1+4m (negative)

1+4m=-4+m

3m=-5

m=-5/3

Equation y=mx +a/m

y=3x/5 + 2/3/5

5y=3x +10/3

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