Question 202800
{{{3x^2+3y^2-24x-12y-15 = 0}}} Divide both sides by 3.
{{{x^2+y^3-8x-4y -5 = 0}}} Group the x- and y-terms as shown:
{{{(x^2-8x)+(y^2-4y)-5 = 0}}} Add 5 to both sides.
{{{(x^2-8x)+(y^2-4y) = 5}}} Complete the square in both the x-terms and the y-terms.
{{{(x^2-8x+16)+(y^2-4y+4) = 5+16+4}}} Factor the left groups ans simplify the right side.
{{{(x-4)^2+(y-2)^2 = 25}}} Compare with the standard form for a circle with center at (h, k) and radius r.
{{{(x-h)^2+(y-k)^2 = r^2}}}
The center is at (4, 2) and the radius is 5.
To graph this circle, we will have to solve this equation for y and the graph each of the two solutions separately.
{{{(x-4)^2+(y-2)^2 = 25}}} Subtract {{{(x-4)^2}}} from both sides.
{{{(y-2)^2 = -(x-4)^2+25}}} Simplify the right side.
{{{(y-2)^2 = -(x^2-8x+16)+25}}}
{{{(y-2)^2 = -x^2+8x-16+25}}}
{{{(y-2)^2 = -x^2+8x+9}}} Take the square root of both sides.
{{{y-2 = sqrt(-x^2+8x+9)}}} The right side should have a + or - sign in front. Add 2 to both sides.
{{{y = 2+-sqrt(-x^2+8x+9)}}} Now graph both of these solutions.
{{{graph(400,400,-2,10,-4,8,2+sqrt(-x^2+8x+9),2-sqrt(-x^2+8x+9))}}}
The y-intercepts are: (0, 5) and (0, -1)
The x-intercepts are: (8.58, 0) and (-0.58, 0)