Question

What is the equation of the circle?

Answer 1

Answer:

○ $\displaystyle (x - 4)^2 + (y + 2)^2 = 25$

Explanation:

Accourding to one of the circle equations, $\displaystyle (x - h)^2 + (y - k)^2 = r^2,$the centre of the circle is represented by $\displaystyle (h, k).$Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared. Now, in case you did not know how to define the radius, you can choose between either method:

Pythagorean Theorem

$\displaystyle a^2 + b^2 = c^2 \\ \\ 4^2 + 3^2 = r^2 \hookrightarrow 16 + 9 = r^2 \hookrightarrow \sqrt{25} = \sqrt{r^2} \\ \\ \boxed{5 = r}$

Sinse we are dealing with length, we only desire the NON-NEGATIVE root.

Distanse Equation

$\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = d \\ \\ \sqrt{[-7 + 4]^2 + [-2 - 2]^2} = r \hookrightarrow \sqrt{[-3]^2 + [-4]^2} = r \hookrightarrow \sqrt{9 + 16} = r; \sqrt{25} = r \\ \\ \boxed{5 = r}$

Sinse we are dealing with distanse, we only desire the NON-NEGATIVE root.

I am joyous to assist you at any time.