# Find the equation of the tangent at the curve 2y= 3x^2 -2x-8 cuts the X axis and show that they make supplementary angles with the x axis

Solving it, we get x = -4/3 and 2

y' = 3x-1

hence, slopes are -5 and 5.

therefore, eqn are:

3y + 15x = 4 and 5x-y = 10

The angles are tan

^{-1}5 and tan

^{-1}-5

tan

^{-1}5 + tan

^{_1}-5 = tan

^{-1}0 = 0 or pi

But tan

^{-1}5 < tan

^{-1}infinity (i. e pi/2)

Therefore tan

^{-1}-5 is negative of an acute angle.

Since an acute angle and its negative cannot complete a full circle (i.e 0), they must be equal to pi.