Question

A tangent to the parabola $y^2=8x$ makes an angle of ${45}^{\circ }$ with the straight line y = 3x + 5 Find its equation and its point of contact

Answer 1

Slope of required tangent's are $\frac{3\pm 1}{1\mp 3}$
$m_1=2,m_2=\frac{1}{2}$
$\therefore$ Equation of tangent of slope m to the parabola $y^2=4ax$ is $y=mx+\frac{a}{m}$
$\therefore$ tangent's $y=-2x-1at(\frac{1}{2},-2)\Rightarrow y=\frac{1}{2}x+4at(8,8)$