Question

A circle is centered at the point (-7, -1) and passes through the point (8, 7).

Answer 1

Answer:

Part 1) The radius of the circle is 17 units

Part 2) The point (-15,14) and (-15,-16) lies on this circle

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance from a circle's center to any point on the circle is called the radius of the circle

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

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

Find the distance (radius) between the points (-7,-1) and (8,7)

substitute in the formula

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

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

$r=\sqrt{(289}\ units$

$r=17\ units$

step 2

Find the equation of the circle in center radius form

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

where

(h,k) is the center of the circle

r is the radius of the circle

we have

$(h,k)=(-7,-1)\\r=17\ units$

substitute

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

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

Remember that

If the point (-15,y) lie on the circle, then the ordered pair must satisfy the equation of the circle

substitute the value of x=-15 in the equation

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

solve for y

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

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

$(y+1)^2=225$

take square root both sides

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

$y=-1+15=14\\y=-1-15=-16$

therefore

The point (-15,14) and (-15,-16) lies on this circle

see the attached figure to better understand the problem