Answer:
\((y-\frac{3}{2})^2=2(x-6)^2\) equation of parabola
Step-by-step explanation:
Focus is (h,k+p)=(6,2)
And directrix y=k-p=1
When comparing the values we get
h=6 and
k+p=2 (a)
k-p=1 (b)
For solving (a) and (b) we substitute k=2-p in (b) we get:
\(2-p-p=1\)
\(2-2p=1\)
\(p=\frac{1}{2}\)
Hence, put \(p=\frac{1}{2}\) in k=2-p we get:
\(k=2-\frac{1}{2}\)
\(k=\frac{3}{2}\)
Now, we have general equation as:
\((y-k)^2=4p(x-h)^2\)
On substituting the values in general equation we get:
\((y-\frac{3}{2})^2=4\frac{1}{2}(x-6)^2\)
\((y-\frac{3}{2})^2=2(x-6)^2\)
