SOLUTION: an ellipse is defined by {{{x^2/81 + y^2/64 = 1}}}. Find the equations of the lines tangent to this ellipse which make and angel of 45 degrees with the x-axis can someone

Question 1016362: an ellipse is defined by . Find the equations of the lines tangent to this ellipse which make and angel of 45 degrees with the x-axis

can someone show me how to do it and answer it. thankyou very much for the help
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Differentiate,

The slope of the tangent line is equal to the value of the derivative.
An angle of 45 degrees is equivalent to a slope of 1.

This point also satisfies the ellipse equation,

Then plugging that into the ellipse equation you get,

So the two points are,
(,)
(,)
That's when the slope is 1.
Similarly when the slope is -1.
(,)
(,)
Use the point slope form of a line to get the equation of the tangent line.

Similarly,

.
.
.

.
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