1. The equation of a circle with center (h,k) and radius r units is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The given circle has center (5,-2) and a radius r=3 units.
We substitute these values into the formula to get:
[tex](x-5)^2+(y--2)^2=3^2[/tex]
This simplifies to:
[tex](x-5)^2+(y+2)^2=9[/tex]
The correct answer is A.
2. The given circle has center (3,-5) and radius r=8 units.
We substitute the given values into the formula to obtain:
[tex](x-3)^2+(y--5)^2=8^2[/tex]
We simplify to get:
[tex](x-3)^2+(y+5)^2=64[/tex]
The correct answer is C
3. The given circle has equation:
[tex](x+8)^2+(y+9)^2=169[/tex]
We can rewrite this equation as:
[tex](x--8)^2+(y--9)^2=13^2[/tex]
Comparing this to
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The center is (-8,-9) and the radius is 13.
The correct answer is A.
4. The given circle has equation:
[tex](x-7)^2+y^2=225[/tex]
We can rewrite this equation as:
[tex](x-7)^2+(y-0)^2=15^2[/tex]
Comparing this to
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The center is (7,0) and the radius is 15.
The correct answer is B.
5. The given circle has center (-2,6) and passes through (-2,10).
We can use the number line to find the radius.
[tex]r=|10-6|=4[/tex]
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We substitute the center and the radius into the formula to get:
[tex](x--2)^2+(y-6)^2=4^2[/tex]
This simplifies to:
[tex](x+2)^2+(y-6)^2=16[/tex]
The correct answer is A
6. The given circle has center (1,2) and passes through (0,6).
We can use the distance formula to find the radius.
[tex]r=\sqrt{(1-0)^2+(2-6)^2}=\sqrt{17}[/tex]
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We substitute the center and the radius into the formula to get:
[tex](x-1)^2+(y-2)^2=\sqrt{17}^2[/tex]
This simplifies to:
[tex](x-1)^2+(y-2)^2=17[/tex]
The correct answer is C
