Question

F Find an equation for a circle san istying the gve a) Center (-1,4), passes through (3,7) Center (-1,4). passes through (3,7

Answer 1

`(x+1)^(2) +(y-4)^(2) =25`

Explanation:

In order to find the equation of the circle, first we need to know the circle's general equation, which is:

`(x-h)^(2) +(y-k)^(2) =r^(2)` where:

(h,k) is the center of the circle and r the radius of the circle.

Because the problem has given the center (-1,4) then h=-1 and k=4.

We need to find now the radius:

Using the distance equation:
`distance=\sqrt{(x2-x1)^(2)+(y2-y1)^(2)}` and because we have the center coordinates and an extra point (3,7) we can find the radius as:

`distance=\sqrt{(3-(-1))^(2)+(7-4)^(2)}`

`distance=\sqrt{4^(2)+3^(2)}`

`distance=√(16+9)`

`distance=√(25)`

`distance=5` which means r=5

In conclusion, the equation for the given circle is
`(x+1)^(2) +(y-4)^(2) =5^(2)` which also, can be written as
`(x+1)^(2) +(y-4)^(2) =25`