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Amiraneli [1.4K]
3 years ago
7

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

n of this circle is (x + )2 + (y + )2 = .
Mathematics
1 answer:
Galina-37 [17]3 years ago
4 0

Answer:

(x+ \boxed{-5})^2+(y+\boxed4)^2=\boxed{100}

Step-by-step explanation:

Given:

Center of circle is at (5, -4).

A point on the circle is (x_1,y_1)=(-3, 2)

Equation of a circle with center (h,k) and radius 'r' is given as:

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

Here, (h,k)=(5,-4)

Radius of a circle is equal to the distance of point on the circle from the center of the circle and is given using the distance formula for square of the distance as:

r^2=(h-x_1)^2+(k-y_1)^2

Using distance formula for the points (5, -4) and (-3, 2), we get

r^2=(5-(-3))^2+(-4-2)^2\\r^2=(5+3)^2+(-6)^2\\r^2=8^2+6^2\\r^2=64+36=100

Therefore, the equation of the circle is:

(x-5)^2+(y-(-4))^2=100\\(x-5)^2+(y+4)^2=100

Now, rewriting it in the form asked in the question, we get

(x+ \boxed{-5})^2+(y+\boxed4)^2=\boxed{100}

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