How do you find the standard equation of a circle

Asked by admin @ 30/10/2021 in Mathematics viewed by 320 People

Determine the equation of a circle with a center at (–4, 0) that passes through the point (–2, 1) by following the steps below. Use the distance formula to determine the radius: Substitute the known values into the standard form: (x – h)² + (y – k)² = r². What is the equation of a circle with a center at (–4, 0) that passes through the point (–2, 1)?

Answered by admin @ 30/10/2021

the equation of a line that has a center at (h,k) and radius of r is

$(x-h)^2+(y-k)^2=r^2$

we can use the distance formula to find the radius ( I would just substitute but whatever)

distance between (-4,0) and (-2,1) is

$D=\sqrt{(-4-(-2))^2+(0-1)^2}$

$D=\sqrt{(-4+2)^2+(-1)^2}$

$D=\sqrt{(-2)^2+1}$

$D=\sqrt{4+1}$

$D=\sqrt{5}$

D=r

so the equation is

$(x-(-4))^2+(y-0)^2=(\sqrt{5})^2$

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

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