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- Homework Statement
- Find the co-ordinates of intersection between tangents that pass through the points ##(-1,7)## and the curve ##y=4-x^2##.

- Relevant Equations
- differentiation

ooops...this was a bit tricky but anyway my approach;

...

##\dfrac{dy}{dx}=-2x##

therefore;

##\dfrac{y-7}{x+1}=-2x##

and given that, ##y=4-x^2## then;

##4-x^2-7=-2x^2-2x##

##x^2+2x-3=0##

it follows that, ##(x_1,y_1)=(-3,-5)## and ##(x_2,y_2)=(1,3)##.

There may be another approach, your insight is welcome guys!.

...

##\dfrac{dy}{dx}=-2x##

therefore;

##\dfrac{y-7}{x+1}=-2x##

and given that, ##y=4-x^2## then;

##4-x^2-7=-2x^2-2x##

##x^2+2x-3=0##

it follows that, ##(x_1,y_1)=(-3,-5)## and ##(x_2,y_2)=(1,3)##.

There may be another approach, your insight is welcome guys!.

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