Question

Use the graph below to determine the equation of the circle in (a) center-radius form and (b) general form.10-(-3,6)(-6,3(0,3)-10(-3,0)1010

Answer 1

Question:

Solution:

An equation of the circle with center (h,k) and radius r is:

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

This is called the center-radius form of the circle equation.

Now, in this case, notice that the center of the circle is (h,k) = (-3,3) and its radius is r = 3 so that the center-radius form of the circle would be:

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

To obtain the general form, we must solve the squares of the previous equation:

`(x+3)^2+(y-3)^2-3^2\text{ = 0}`

this is equivalent to:

`(x^2+6x+3^2)+(y^2-6y+3^2)\text{ - 9 = 0}`

this is equivalent to

`x^2+6x+9+y^2-6y\text{ = 0}`

this is equivalent to:

`x^2+y^2+6x-6y\text{ +9= 0}`

so that, the general form equation of the circle would be:

`x^2+y^2+6x-6y\text{ +9= 0}`

thus, the correct answer is:

CENTER - RADIUS FORM:

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

GENERAL FORM:

`x^2+y^2+6x-6y\text{ +9= 0}`