First thing's first, let's find the formula for the slope of any tangent line to the curve, we get that from the derivative:

So every tangent to the curve will have the slope -2x. So use that for our m.

Now we have by the point-slope form, that

Using and , we get:

------> equation for any tangent to the curve

Now, want all lines that intersect with the curve , so we equate the general formula for the tangent line to the formula for the curve, we get:

Using each of these values, we can get a different m

when ,

when ,

Again going back to the point-slope form, using and and , we get:

Tangent line 1:

Tangent line 2:

Below is a picture of what's going on

Questions very similar to this were done yesterday. See if you can read through the threads and understand what was done. it's not that hard to understand, you're bound to get one of the explanations2. Find the point on the curve where the tangent line is perpendicular to the line 6x+y-5=0.

http://www.mathhelpforum.com/math-he...d-tangent.html

http://www.mathhelpforum.com/math-he...gent-line.html