Question

PLS HELP!!

Answer 1

Answer:

Part 1) The radius of the circle is $17\ units$

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

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

substitute the values

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

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

$r=\sqrt{289}}$

$r=17\ units$

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

$(x+7)^{2}+(y+1)^{2}=17^{2}$ -----> equation of the circle in center radius form

substitute the value of x=-15 in the equation and solve for y

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

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

$(y+1)^{2}=289-64$

$(y+1)^{2}=225$

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

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

so

$y=14$

$y=-16$

therefore

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

see the attached figure to better understand the problem