Question

Which of these correctly represents a circle with acenter of (5,-4) and a radius of 7?

Answer 1

The equation for the circle with center at (a, b) and with radius r is written as

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

The center point of the circle is given in the problem with the coordinates (5, -4) and the circle has a radius of 7. We have a = 5, b = -4, and r = 7. We substitute these values on the equation of the circle stated above, we get

$(x-5)^2+(y-(-4))^2=7^2_{}$

Simplifying the equation, we get

$(x-5)^2+(y+4)^2=49$

which is the equation of the circle given in the problem.