Question

Write the equation of the parabola with the given conditions.A. focus (0,1) and directrix x = 3.B. vertex (2,4) and focus (0,4)vertex is (2,4) so h = 2 and k = 4; focus (h + p,k) = (0,4)

Answer 1

we have the following:

A.

`\begin{gathered} \mleft(x-h\mright)^2=4p\cdot\mleft(y-k\mright) \\ focus(0,1) \\ directrix,x=3. \\ p=(1)/(2) \\ k=1 \\ h=0 \\ (x-0)^2=4(1)/(2)\cdot(y-1)\text{ } \\ x^2=2\cdot(y-1)\text{ } \end{gathered}`

B.

`\begin{gathered} (x-h)^2=4p\cdot(y-k) \\ focus(0,1) \\ vertex(2,4) \\ p=2-0=2 \\ h=2 \\ k=4 \\ (x-2)^2=4\cdot2\cdot(y-4) \\ (x-2)^2=8\cdot(y-4) \end{gathered}`