Question

what transformation is needed to write the equation $x^{2}+y^{2}-6x + 4y + 9 = 0$ in standard form?
a. complete the square
b. factor the equation
c. combine like terms
d. distribute terms
which radius corresponds to the circle with the equation $(x + 5)^{2}+(y - 1)^{2}=121$?
a. 12
b. 13
c. 121
d. 11

Explanation:

Step1: Recall the standard form of a circle equation

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

Step2: Compare with the given equation \((x + 5)^2+(y - 1)^2=121\)

We know that \(r^2 = 121\).

Step3: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{121}\).

Answer:

\(11\)