Answer:
Part 1) The radius of the circle is [tex]17\ units[/tex]
Part 2) The points (15,14) and (-15,-16) lies on this circle
Step-by-step explanation:
Part 1
we know that
The distance between the center of the circle at point (-7,-1) and the point (8,7) is equal to the radius of the circle
so
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[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]
Part 2
we know that
If the point (-15,y) lies on the circle, then the ordered pair must be satisfy the equation of the circle
The equation of the circle is equal to
[tex](x+7)^{2}+(y+1)^{2}=17^{2}[/tex] -----> equation of the circle in center radius form
substitute the value of x=-15 in the equation and solve for y
[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]
[tex]y+1=(+/-)15[/tex]
[tex]y=-1(+/-)15[/tex]
so
[tex]y=14[/tex]
[tex]y=-16[/tex]
therefore
The points (15,14) and (-15,-16) lies on this circle
see the attached figure to better understand the problem
Answer:
Part 1) The radius of the circle is
Part 2) The points (15,14) and (-15,-16) lies on this circle
Step-by-step explanation:
