Question

Which equation represents a circle with the same radius as the circle shown but with a center at (-1,1)

Answer 1

The equation of the circle is:

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

or

`x^2+y^2+2x-2y=14`

Explanation:

The radius of the given circle as represented in the graph is: 4 units.

The center of a circle is: (-1,1)

We know that the equation of a circle with center (h,k) and radius r is given by:

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

We have:

r=4 and (h,k)=(-1,1)

Hence, the equation of circle is:

`(x+1)^2+(y-1)^2=4^2\\\\\\x^2+1+2x+y^2+1-2y=16\\\\x^2+y^2+2x-2y=14`

Hence, equation is:

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

or

`x^2+y^2+2x-2y=14`

Answer 2

(x + 1)² + (y - 1)² = 16

Explanation:

Since the standard form for an equation of a circle is

(x - h)² + (y - k)² = r²

The (h,k) are co-ordinate of your centre of circle, which in this case is (-1,1) and r is the radius of circle.

As we can see in the figure radius = 4units

from centre(1,-2) to (1,-2)

Put these into the equation

(x + 1)² + (y - 1)² = 4²

(x + 1)² + (y - 1)² = 16