33. What values of the constants a, b, and c make the ellipse
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Differentiate both sides of the equation of the circle with respect to , treating
as a function of
:
This gives the slope of any line tangent to the circle at the point .
Rewriting the given line in slope-intercept form tells us its slope is
In order for this line to be tangent to the circle, it must intersect the circle at the point such that
In the equation of the circle, we have
If , then
, so we omit this case.
If , then
, as expected. Therefore
is a tangent line to the circle
at the point (1, -2).