Question

Write the equation in standard form for the circle with center (0, 9) passing through (0, 27/2)

Answer 1

Given

coordinates of center= (0,9)

Circle passes through (0, 27/2)

Find

Equation of circle

Explanation

The equation of circle in standard form is

$\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-0)^2+(y-9)^2=r^2 \end{gathered}$

We know the circle passes through (0,27/2), then

$\begin{gathered} (0-0)^2+(\frac{27}{2}-9)^2=r^2 \\ r=4.5 \end{gathered}$

So the equation in the standard form is

$(x-0)^2+(y-9)^2=4.5^2$

Final Answer

$(x-0)^2+(y-9)^2=4.5^2$