Question

the vertex is at(-5,1), and the focus is at(2,1). write the equation and graph.

Answer 1

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Answer 2

distance between vertex & focus= \[\sqrt{(-5-2)^{2}+(1-1)^{2}}= 7\]
equation of the axis of the parabola-
\[y=1\]
so, equation of directrix would be-
x = k (k is arbitrary constant to be determined)

now, since the directrix is equidistant from vertex as focus,

\[(-5-k)/\sqrt{1^{2}}=7\]
so, k=-12

so the directrix is x+12=0

so the equaton of the parabola is \[(x+12)/\sqrt{1^{2}}=\sqrt{(x-2)^{2}+(y-1)^{2}}\]

Answer 3

equation:
\[x = \frac{1}{28}(y-1)^{2}-5\]