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Type the correct answer in each box. A circle is centered at the point (5, -4) and passes through the point (-3, 2).


The equation of this circle is (x + )2 + (y + )2 =

Verified Answer :

caylus

Hello,

C=(5,-4)
P=(-3,2)
|CP|²=(-3-5)²+(2+4)²=64+36=100

(x-5)²+(y+4)=100

Remember the  equation of the circle:

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

where \((h,k)\) is the center of the circle and \(r\) is its radio.

You already have the center, that is \((h,k)=(5,-4)\) and hence we have

\(h=5\) and \(k=-4\) (be careful with the signs).

For the radio we use the formula of distance between two points:

\(r^2 = (-3-5)^2 + (2-(-4))^2= 64 + 36 = 100 = 10 ^2\)

So the radio is 10.

Finally we replace tha data in the equation of the circle to obtain:

\((x-5)^2 + (y-(-4))^2=10^2\\\\(x-5)^2 + (y+4)^2=10^2\)

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