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Type the correct answer in each box.

A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is
units. The point (-15,
) lies on this circle.

Type the correct answer in each box. A circle is centered at the point (-7, -1) and-example-1

1 Answer

7 votes

Answer:

Part 1) The radius is
r=17\ units

Part 2) The points (-15,14) and (-15,-16) lies on the circle

Explanation:

step 1

Find the radius of the circle

we know that

The distance from the center to any point on the circumference is equal to the radius.

we have


(-7,-1),(8,7)

Find the distance

the formula to calculate the distance between two points is equal to


d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}

substitute


r=\sqrt{(7+1)^(2)+(8+7)^(2)}


r=\sqrt{(8)^(2)+(15)^(2)}


r=√(289)


r=17\ units

step 2

The point (-15,y) lies on the circle

we know that

If a ordered pair lie on the circle, them the ordered pair must satisfy the equation of the circle

The equation of the circle is


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

The center is (-7,-1) an the radius is 17 units

substitute


(x+7)^(2)+(y+1)^(2)=17^(2)


(x+7)^(2)+(y+1)^(2)=289

substitute the x-coordinate of the point and solve for the y-coordinate

For x=-15


(-15+7)^(2)+(y+1)^(2)=289


(-8)^(2)+(y+1)^(2)=289


64+(y+1)^(2)=289


(y+1)^(2)=289-64


(y+1)^(2)=225

square root both sides


(y+1)=(+/-)15


y=-1(+/-)15


y=-1(+)15=14


y=-1(-)15=-16

therefore

The points (-15,14) and (-15,-16) lies on the circle

see the attached figure to better understand the problem

Type the correct answer in each box. A circle is centered at the point (-7, -1) and-example-1
User Belizzle
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