Question

Write the standard form of the equation and the general form of the equation of the circlewith radius r and center (h.k). Then graph the circle.r= 10; (h,k) = (8,6)The standard form of the equation of this circle isThe general form of the equation of this circle is(Simplify your answer.)Graph the circle.-20 -18Click toenlargegraph

Answer 1

To solve this problem, we will first find the standard form of the circle equation. Given a circle of radius r and center (h,k), the standard form of the circle equation would be

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

In our case, we have h=8 , k=6 and r=10. So the equation for the given circle would be

`(x-8)^2+(y-6)^2=10^2=100`

The general form of the circle equation can be obtained from expanding the squares on the left side of the equality sign. Recall that

`(a-b)^2=a^2-2a\cdot b+b^2`

So, applying this to the standard equation we get

`(x-8)^2=x^2-16x+64`
`(y-6)^2=y^2-12y+36`

So our equation becomes

`x^2-16x+64+y^2-12y+36=100`

Operating on the left side, we have

`x^2-16x+y^2-12y+100=100`

By subtracting 100 on both sides, we get

`x^2-16x+y^2-12y=0`

which the general form of the equation of the given circle.

Using a graphing tool, we have that the circle's graph would be