Question

Find the equations of tangents to the parabola y^2=4ax which are equally inclined to the coordinate axis.​

Answer 1

The equations of tangents to the parabola y^2 = 4ax which are equally inclined to coordinate axes are x - y + a = 0, x + y + a = 0.

• Given parabola,

                              $y^{2}=4ax------(1)$

• We know that equation of tangent to parabola (1) is given by

                             $y=mx+\frac{a}{m}-----(2)$

• The tangents are equally inclined to the coordinate axes

                             ⇒ m = ± 1

• Substituting 'm' in (2), we get

          m = 1                             m = - 1

         y = x + a                         y = - x - a

        x - y + a = 0                    x + y + a = 0