Question

If the equation of a circle is given by $x^2 + y^2 - 8x + 10y - 12 = 0$, what is the center of the circle?

• A. (4,5)
• B. (4,-5)
• C. (4,5)
• D. (4,-5)

Answer 1

Answer: (B)

(4, -5)

Answer 2

The general equation of a circle is given by $x^2 + y^2 + 2gx + 2fy + c = 0$, where the center of the circle is $(-g, -f)$.

Given the equation of the circle: $x^2 + y^2 - 8x + 10y - 12 = 0$.

Comparing this with the general form: $2g = -8 \Rightarrow g = -4$ $2f = 10 \Rightarrow f = 5$

The center of the circle is $(-g, -f)$. Substituting the values of $g$ and $f$: Center $= (-(-4), -(5)) = (4, -5)$.

Therefore, the center of the circle is $(4, -5)$.