Question

What is the equation of the circle with a center at `(-4 ,2 )` and a radius of `7`?

Answer 1

The equation you're looking for is `(x+4)^2+(y-2)^2=7^2`.

Explanation:

The standard equation for a circle is as follows:

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

where h and k are the x and y coordinates of the circle's centre, respectively, and r is the radius of the circle.

In your problem, your h value is negative, so the two negatives cancel out and make a positive 4.

Answer 2

`(x+4)^2+(y-2)^2=49`

Explanation:

`"the equation of a circle in standard form is"`

`color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))`

`"where "(a,b)"are the coordinates of the centre and r"`
`"is the radius"`

`"here "(a,b)=(-4,2)" and "r=7`

`rArr(x-(-4))^2+(y-2)^2=7^2`

`rArr(x+4)^2+(y-2)^2=49larrcolor(red)"equation of circle"`