Question

(07.03 MC)A circle is represented by the equation (x + 7)2 + (y - 9)2 = 144.Which of the following statements is true?O The circle is centered at (-7, 9) and has a diameter of 12.O The circle is centered at (-7, 9) and has a radius of 12.O The circle is centered at (7,-9) and has a diameter of 12.O The circle is centered at (7, -9) and has a radius of 12.

Answer 1

The general equation of a circle is,

$(x-a)^2+(y-b)^2=r^2$

The equation given is,

$(x+7)^2+(y-9)^2=144$

Comparing the two equations together

$\begin{gathered} -a=7 \\ \frac{-1a}{-1}=\frac{7}{-1} \\ a=-7 \\ \\ b=9 \\ \\ r^2=144 \\ r=\sqrt{144}=12 \end{gathered}$

Hence, Option 2 the circle is centered at (-7, 9) and has a radius of 12.