Question

Which equation represents the circle described?

The radius is 2 units.
The center is the same as the center of a circle whose equation is
x²+ y²– 8x – 6y + 24 = 0.

a.) (x + 4)²+ (y + 3)²= 2
b.) (x – 4)² + (y – 3)² = 2
c.) (x – 4)² + (y – 3)²= 2²
d.) (x + 4)² + (y + 3)² = 2²

Answer 1

the right answer is c)

Explanation:

Answer 2

We have the equation:

`x^2+y^2-8x-6y+24=0`

By arranging this equation in terms of x and y, we have:

`x^2-8x+y^2-6y=-24 \\ \\`

By using the method of completing the square, we have:

`x^2-8x+\mathbf{\left((8)/(2)\right)^2}+y^2-6y+\mathbf{\left((6)/(2)\right)^2}=-24+\mathbf{\left((8)/(2)\right)^2}+\mathbf{\left((6)/(2)\right)^2} \\ \\ x^2-8x+\mathbf{16}+y^2-6y+\mathbf{9}=-24+\mathbf{16}+\mathbf{9} \\ \\ \boxed{(x-4)^2+(x-3)^2=1}`

The center of this circle is:

`(h,k)=(4,3)`

So the equation that fulfills the statement is:

`(x-4)^2+(y-3)^2=2^2`

Finally, the right answer is c)