2 tangents to y = x2-2x-3 pass thru (5,3); find pts, eqns

[ashliecg]

Two tangents to y=x2-2x-3 pass through (5,3). Fine the points of tangency and write the equations of the tangent lines.

 

[galactus]

Re: 2 tangents to y = x2-2x-3 pass thru (5,3); find pts, eqn

Two tangents to \(\displaystyle y=x^{2}-2x-3\) pass through (5,3). Fine the points of tangency and write the equations of the tangent lines.

They tell you a 'passes through' point, but you don't know where it's tangent.

You can use \(\displaystyle \L\\y-y_{1}-m(x-x_{1})\)

You're given y, y1, x1. You can find the slope by taking the derivative of y. Then you have m. Sub everything in and solve for x. You will get two solutions. Then find your line equations from those.