# Prove that the angle between tangents from (-2,3) to y2 = 8x are at right angles.

Prove that the angle between tangents from (-2,3) to y2 = 8x are at right angles.

1694

Here, the given equation of parabola is y2= 8x.

The equation of tangent to the parabola y2=8x is,

y= mx + 2/m

This tangent passes through the point (-2, 3)

So,       3 = -2m + 2/m

or,  3m + 2m2 = 2

or,   2m2 + 3m - 2 = 0

or,   2m2 + (4 - 1)m -2 = 0

or,   2m2 + 4m - m - 2 = 0

or,   2m(m + 2) - 1(m+2) = 0

or,   (m + 2) (2m - 1) = 0

Either,                       Or,

m = -2                  m = 1/2

Required angle is,

Prove that the angle between tangents from (-2,3) to y2 = 8x are at right angles.

Here, the given equation of parabola is y2= 8x.

The equation of tangent to the parabola y2=8x is,

y= mx + 2/m

This tangent passes through the point (-2, 3)

So,       3 = -2m + 2/m

or,  3m + 2m2 = 2

or,   2m2 + 3m - 2 = 0

or,   2m2 + (4 - 1)m -2 = 0

or,   2m2 + 4m - m - 2 = 0

or,   2m(m + 2) - 1(m+2) = 0

or,   (m + 2) (2m - 1) = 0

Either,                       Or,

m = -2                  m = 1/2

Required angle is,