Thread: Find the equation of both lines?

Determine the equation of both lines that are tangent to the graph of y=x^2 +4 and pass through the point (1,-2)

So would I simply use the y=mx+b form, m=2, y= -2, and x = 1?

Originally Posted by RyGuy

Determine the equation of both lines that are tangent to the graph of y=x^2 +4 and pass through the point (1,-2)

So would I simply use the y=mx+b form, m=2, y= -2, and x = 1?

no ... the point (1,-2) does not lie on the parabola.

Originally Posted by skeeter

no ... the point (1,-2) does not lie on the parabola.

Oh right.

So then how would I go about this?

Originally Posted by RyGuy

Determine the equation of both lines that are tangent to the graph of y=x^2 +4 and pass through the point (1,-2)

So would I simply use the y=mx+b form, m=2, y= -2, and x = 1?

the derivative of the parabola equation gives the slope of all tangent lines to the curve.

You need the equations of the two that pass through (1,-2).

hence, write the derivative to get the slopes of these lines.
then use

point of tangency on the curve is

each tangent line passes thru the point

remember how to find the slope between two points?

... also, note that the slope of both tangent lines is y' = 2x

I'll let you take it from here.