# What are the equations of the tangent lines out P(2,1) to the parabola with equation #y = x^2#? Thank you!

##### 1 Answer

Jun 11, 2018

Two tangents

#y = 2(2-sqrt 3)x-7+4sqrt3# #y = 2(2+sqrt 3)x-7-4sqrt3#

#### Explanation:

The tangent to a curve

For

with

For the tangent to go through

So, there are two tangents to the parabola from

- for
#x_0 = 2-sqrt 3# ,#y = 2(2-sqrt 3)x-7+4sqrt3# - for
#x_0 = 2+sqrt 3# ,#y = 2(2+sqrt 3)x-7-4sqrt3#