Answer:
Part 1) The radius of the circle is r=17 units
Part 2) The points (-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 between the center of the circle and any point on the circle is equal to 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]
we have
(-7, -1) and (8, 7)
substitute
[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}[/tex]
[tex]r=\sqrt{(8)^{2}+(15)^{2}}[/tex]
[tex]r=\sqrt{289}[/tex]
[tex]r=17\ units[/tex]
step 2
Find out the y-coordinate of point (-15,y)
The equation of the circle in standard form is equal to
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where
(h,k) is the center
r is the radius
substitute the values
[tex](x+7)^2+(y+1)^2=17^2[/tex]
[tex](x+7)^2+(y+1)^2=289[/tex]
Substitute the value of x=-15 in the equation
[tex](-15+7)^2+(y+1)^2=289[/tex]
[tex]64+(y+1)^2=289[/tex]
[tex](y+1)^2=289-64[/tex]
[tex](y+1)^2=225[/tex]
square root both sides
[tex](y+1)=(+/-)15[/tex]
[tex]y=-1(+/-)15[/tex]
[tex]y=-1(+)15=14[/tex]
[tex]y=-1(-)15=-16[/tex]
therefore
we have two solutions
point (-15,14) and point (-15,-16)
see the attached figure to better understand the problem
