Question

Determine the equation of the circle with radius √91 and center (3, -2).

Answer 1

• (x-3)² + (y+2)² = 91

Explanation:

To find:-

• The equation of the circle.

Answer:-

We are here given that the radius of the circle is √91 units and its centre is (-3,2) .

We know that the standard equation of circle is,

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

where,

• (h,k) is the centre.
• r is the radius.

On substituting the respective values, we have;

`\longrightarrow \{ x-3\}^2+\{ y-(-2)\}^2= (\sqrt91)^2 \\`

Simplify,

`\longrightarrow \red{ (x-3)^2+(y+2)^2=91} \\`

This is the required equation of the circle.

Answer 2

(x - 3)² + (y + 2)² = 91

Explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (3, - 2 ) and r =
`√(91)` , then

(x - 3)² + (y - (- 2) )² = (
`√(91)` )² , that is

(x - 3)² + (y + 2)² = 91 ← equation of circle