Coordinate Geometry of Circles

State the equation of a circle with centre (h, k) radius, r and diameter, d = 2r.

What is the equation of a circle centered at (–6, 8) with a radius of 9?

• (x + 6)² + (y – 8)² = 3

• (x – 6)² + (y + 8)² = 81

• (x + 6)² + (y – 8)² = 81

• (x – 6)² + (y + 8)² = 9

For the equation (x – 2)² + (y – 5)² = 12, what is the length of the diameter?

• 4√3

• 12

• 24

• 144

The point (-5,6) is on a circle with center (-1,3) write the equation of the circle

• (x+1)² + (y-3)²= 4000

• (x+5)² + (y-0)²= 25

• (x+1)² + (y-3)²= 25

• (x-1)² + (y+3)²= 25

If the center of a circle is: (-4,2) and the radius is 6, what is the equation of the circle?

What is the equation for this circle?

• (x+1)+(y+1)=9

• x²+y²=9

• x+y=9

Answer explanation

The correct equation for a circle is x²+y²=r², where r is the radius. In this case, the equation x²+y²=9 represents the circle with a radius of 3.

Determine the equation of a circle with center (5,-3) and radius of 9

• x²+y²-10x+6y-47=4

• x²+y²-10x-6y-47=0

• 2x²+y²+10x+6y-47=0

• x²+y²-10x+6y-47=0

Answer explanation

The equation of a circle with center (5,-3) and radius of 9 is x^2 + y^2 - 10x + 6y - 47 = 0.

There was an earthquake in a city. It was felt up to 80 miles from its epicenter. If the epicenter can be located at the point (15, 8) on a coordinate plane, which equation would help to find the boundary of the area that is affected by the earthquake?

• (x – 15)² + (y – 8)² = 80

• (x – 15)² + (y – 8)² = 289

• (x + 15)² + (y + 8)² = 529

• (x – 15)² + (y – 8)² = 80²