SOLUTION: Find the cooordinates of the two points on the curve y=4-x^2 whose tangents pass through the point (-1,7)

Question 978015: Find the cooordinates of the two points on the curve y=4-x^2 whose tangents pass through the point (-1,7)
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
The line minus the parabola should have ONE solution. Each of these lines must have slope -2x, using derivative for the given parabola equation.

, equation for the tangent lines in point-slope form.
-----Again this is a TANGENT LINE, not a parabola. We do not have yet any value for the slope.
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This line must intersect the parabola in ONLY ONE POINT. Their difference must be zero for only one value of x.

, difference between line and parabola.

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One value where tangent on the parabola is x=1; and the other value where tangent on parabola is x=-3.

FIND CORRESPONDING y VALUES ON PARABOLA
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The points where line is tangent to parabola and tangent includes (-1,7) are (1,3) and (-3,-5).

You can make a sketch, graph on your own to be more certain.
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