Write the equation of a parabola with a vertex at (-3, 7) and a directrix x = -8.

Question

katherinesmith · Answer

@tkhunny

tkhunny · Answer

With the vertex and directrix, the focus should be trivial.  Where is it?

tkhunny · Answer

With the vertex and directrix, "p" should be trivial along with 4p.  What is "p"?

katherinesmith · Answer

wait jump ahead a couple of steps. is the equation $$y - 7 = \frac{ 1 }{ 20 }(x + 3)^{2}$$

tkhunny · Answer

No.  That opens UP and you should be opening RIGHT.  You do have p and the vertex.

katherinesmith · Answer

so $$x + 3 = \frac{ 1 }{ 20 }(y - 7)^{2}$$

tkhunny · Answer

That's better.  Do you believe it?

katherinesmith · Answer

i think so.

tkhunny · Answer

You can ALWAYS check with the definition.  With directrix at x = -8 and focus at (2,7), an application of the definition of a parabola should have the same result.

Good work.