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
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance (radius) between the points (-7,-1) and (8,7)
substitute in the formula
[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}[/tex]
[tex]r=\sqrt{(8)^{2}+(15)^{2}}[/tex]
[tex]r=\sqrt{(289}\ units[/tex]
[tex]r=17\ units[/tex]
step 2
Find the equation of the circle in center radius form
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where
(h,k) is the center of the circle
r is the radius of the circle
we have
[tex](h,k)=(-7,-1)\\r=17\ units[/tex]
substitute
[tex](x+7)^2+(y+1)^2=17^2[/tex]
[tex](x+7)^2+(y+1)^2=289[/tex]
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
[tex](-15+7)^2+(y+1)^2=289[/tex]
solve for y
[tex](-8)^2+(y+1)^2=289[/tex]
[tex]64+(y+1)^2=289[/tex]
[tex](y+1)^2=225[/tex]
take square root both sides
[tex]y+1=(+/-)15\\y=-1(+/-)15[/tex]
[tex]y=-1+15=14\\y=-1-15=-16[/tex]
therefore
The point (-15,14) and (-15,-16) lies on this circle
see the attached figure to better understand the problem
