A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is ? units. The point (-7, ?) lies on this circle.

Hello,

The circle has like equation: (x+3)²+(y-2)²=r²

If x=1 then y=5 ==>(1+3)²+(5-2)²=r²==>4²+3²=r²==>r=5 (the radius)

if x=-7 then (-7+3)²+(y-2)²=25 ==> (y-2)²=25-16==>y=2+3 or y=2-3
The points (-7,5) and (-7,-1) are on the circle.

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jainveenamrata jainveenamrata · Answer 2 · 2022-07-04T08:06:05+02:00

The radius of the circle will be 5 units and the point (-7, 1) lies on this circle.

What is an equation of a circle?

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x – h)² + (y – k)² = r²

A circle is centered at the point (-3, 2).

(x + 3)² + (y – 2)² = r²

The circle passes through the point (1, 5) will be

r² = (1 + 3)² + (5 – 2)²

r² = 4² + 3²

r² = 25

r = 5

Then the equation will be

(x + 3)² + (y – 2)² = 5²

(x + 3)² + (y – 2)² = 25

The point (-7, y) lies on this circle. Then the value of y will be

(- 7 + 3)² + (y – 2)² = 25

16 + (y – 2)² = 25

(y – 2)² = 9

y – 2 = 3

y = 1

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