Show that the tangent to the parabola Y=Ax^2 (for A does not equal 0) at the point where x = c will intersect the x axis at the point (c/2 , 0 . Where does it intersect the y axis.

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- Jan 8th 2006, 08:18 AMfrozenflamesx-intercept of tangent to parabola
Show that the tangent to the parabola Y=Ax^2 (for A does not equal 0) at the point where x = c will intersect the x axis at the point (c/2 , 0 . Where does it intersect the y axis.

- Jan 8th 2006, 09:07 AMThePerfectHackerQuote:

Originally Posted by**frozenflames**

Thus, the slope of the tangent line is $\displaystyle m=2ac$. Now use the formula for finding equations of line by knowing thier slopes and the point that they pass through. That formula is $\displaystyle y-y_0=m(x-x_0)$this tangent line has slope $\displaystyle m=2ac$ and passes through the point of tangentcy $\displaystyle x=c$ thus $\displaystyle y=ac^2$ Thus, the equation of the tangent line is $\displaystyle y-ac^2=2ac(x-c)$ thus, $\displaystyle y=2acx-2ac^2+ac^2=2acx-ac^2$ now set $\displaystyle y=0$ because this is the x-intercept thus $\displaystyle 2acx-ac^2=0$ solve for $\displaystyle x$ thus$\displaystyle x=c/2$

Q.E.D. - Jan 8th 2006, 09:16 AMfrozenflames
Where does it intersect the y Axis?

- Jan 8th 2006, 09:22 AMThePerfectHackerQuote:

Originally Posted by**frozenflames**

Q.E.D.