Question

Type the correct answer in each box.

Answer 1

Answer:

Part 1) The radius is $r=17\ units$

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

Step-by-step explanation:

The correct question is

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

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

$r=\sqrt{(7+1)^{2}+(8+7)^{2}}\\r=\sqrt{(8)^{2}+(15)^{2}}\\r=\sqrt{289}\\r=17\ units$

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

$(y+1)=\pm15\\y=-1\pm15\\y=-1(+)15=14\\y=-1(-)15=-16$

therefore

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

see the attached figure to better understand the problem