Question

write the equation for the circle with center (0,0) that passes through the point (9,7).
the equation of the circle is. (be sure to enter the equation of the circle)

Explanation:

Step1: Recall standard circle equation

The standard equation of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Determine center and radius

Given center \((0,0)\), so \(h = 0,k = 0\). The circle passes through \((9,7)\). Use the distance formula \(r=\sqrt{(x - h)^2+(y - k)^2}\). Substitute \(x = 9,y = 7,h = 0,k = 0\), then \(r=\sqrt{(9 - 0)^2+(7 - 0)^2}=\sqrt{81 + 49}=\sqrt{130}\).

Step3: Write the circle equation

Substitute \(h = 0,k = 0,r^2 = 130\) into \((x - h)^2+(y - k)^2=r^2\), we get \(x^2+y^2=130\).

Answer:

\(x^2 + y^2=130\)