Question

What is the equation of the circle with: center (5, 7) and point on the circle: (-2, 8)

Answer 1

Answer:

$(x-5)^2+(y-7)^2=50$

Step-by-step explanation:

Hi there!

Equation of a circle: $(x-h)^2+(y-k)^2=r^2$ where the circle is centered at $(h,k)$ and r is the radius

Plug in the center (5,7)

$(x-5)^2+(y-7)^2=r^2$

Plug in the given point (-2,8) to solve for r²

$(-2-5)^2+(8-7)^2=r^2\\(-7)^2+(1)^2=r^2\\49+1=r^2\\50=r^2$

Therefore, r² is equal to 50. Plug this back into $(x-5)^2+(y-7)^2=r^2$

$(x-5)^2+(y-7)^2=50$

I hope this helps!