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 how many units. The point (-7,? ) lies on this circle.

Accepted Solution

A:

we know that

the equation of a circle is

(x-h)²+(y-k)²=r²

(h,k) is the center----------> (-3,2)

the radius is the distance point (-3,2) and point (1, 5)

d=√(5-2)²+(1+3)²-------> d=√9+16----------> d=5

radius=5 units

equation is

(x+3)²+(y-2)²=25

for x=-7

(-7+3)²+(y-2)²=25-------> 16+y²-4y+4=25

y²-4y-5=0

using a graph tool -------> to resolve the second order equation

see the attached figure

the solution is

y1=-1

y2=5

the point will be

(-7,-1)

(-7,5)

the equation of a circle is

(x-h)²+(y-k)²=r²

(h,k) is the center----------> (-3,2)

the radius is the distance point (-3,2) and point (1, 5)

d=√(5-2)²+(1+3)²-------> d=√9+16----------> d=5

radius=5 units

equation is

(x+3)²+(y-2)²=25

for x=-7

(-7+3)²+(y-2)²=25-------> 16+y²-4y+4=25

y²-4y-5=0

using a graph tool -------> to resolve the second order equation

see the attached figure

the solution is

y1=-1

y2=5

the point will be

(-7,-1)

(-7,5)