# Two tangents to the parabola #y=1-x^2# intersect at point #(2,0)#. Find the coordinates of points on parabola on which these are tangents?

##### 1 Answer

Coordinates are

#### Explanation:

Equation of a line with slope

As this line will normally have two common points with the parabola

The two roots of this equation will give two points, but for a tangent, we need two coincident points i.e. roots should be equal, which is possible only when determinant is zero.

Hence, for tangent, we should have

i.e.

wich gives us two values of

Hence we have two equations of tangents

graph{(y+(4+2sqrt3)(x-2))(y+(4-2sqrt3)(x-2))(y-1+x^2)=0 [-8.585, 11.415, -8.4, 1.6]}

Coordinates will be given by

which gives

and

which gives

Hence coordinates are