Question

what is the radius in the equation below?
$(x - 2)^2 + (y + 5)^2 = 144$

• $-2$
• $5$
• $12$
• $144$

Explanation:

Step1: Recall circle equation form

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

Step2: Compare with given equation

Given equation: \((x - 2)^2 + (y + 5)^2 = 144\). Here, \(r^2 = 144\).

Step3: Solve for \(r\)

Take the square root of \(144\): \(r=\sqrt{144}=12\).

Answer:

12