Question

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

The equation of this circle is (x + ___)2 + (y + ___)2 = ___

Answer 1

you have to use the distance formula in order to find the radius. By doing that you get the answer 10. so the equation is:

(x-4)^2 + (y+5)^2 = 10

Answer 2

Answer:
`(x-5)^2+(y+4)^2=100`

Explanation:

We know that the general equation of a circle can be written as :

`(x-h)^2+(y-k)^2=r^2` (1), where (center )= (h,k) and r= radius

As per given , we have

(h,k) = (5,-4)

(x,y) =(-3,2)

Substitute these value in equation (1), we get

`(-3-5)^2+(2-(-4))^2=r^2\\\\\Rightarrow\ (-8)^2+(2+4)^2=r^2\\\\\Rightarrow\ 64+6^2=r^2\\\\\Rightarrow\ 64+36=r^2\\\\\Rightarrow\ 100=r^2\\\\\Rightarrow\ r=√(100)=\pm10`

Since radius cannot be negative , thus r= 10 units

Put value of
`r^2` and (h,k) in equation (1), we get

`(x-5)^2+(y+4)^2=100`

Thus , the equation of given circle is
`(x-5)^2+(y+4)^2=100`.