MATH SOLVE

4 months ago

Q:
# A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is ? units. The point (-7, ? ) lies on this circle.

Accepted Solution

A:

Answer:The radius of the circle is 5 units(-7,-1) and (-7,5) lies on the circleStep-by-step explanation:A circle is centered at the point (-3, 2) and passes through the point (1, 5). Center of the circle is given as (-3,2)Use center radius form of the circle equation(x-h)^2 + (y-k)^2 = r^2(h,k) is the center and r is the radiush= -3 and k = 2, point (x,y) is (1,5)[tex](1+3)^2+(5-2)^2= r^2[/tex]16+9 = r^225= r^2 so radius r= 5The radius of the circle is 5 unitsequation of circle is (x+3)^2 + (y-2)^2 = 25To find out the point we plug in -7 for x(-7+3)^2 + (y-2)^2 = 2516 + (y-2)^2 = 25Subract 16 from both sides+ (y-2)^2 = 9take square root on both sidesy-2=+-3y= +3+2= 5y= -3+2= -1So (-7,-1) and (-7,5) lies on the circle