SOLUTION: please help me to solve this problem: Find the equation of the tangent to the hyperbola x^2-4y^2=36 which is perpendicular to the line x-y+4=0

Question 983166: please help me to solve this problem:
Find the equation of the tangent to the hyperbola x^2-4y^2=36 which is perpendicular to the line x-y+4=0
Thanks a lot
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
A line perpendicular to would have a slope that is the negative reciprocal of its slope.

So the slope of the perpendicular line would be .
.
.
.
The tangent line to the hyperbola can be found by differentiating,

.
.
.
This slope must equal the previously calculated slope,

So then,

The two points of intersection are,
(,) and (,)
So then using the point-slope form of a line,
and
and
.
.
.

.

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