Question

State the center and radius of each circle. then write the equation of the circle in standard form.

See attached:

Answer 1

#1

• Centre(-2,3)
• Radius=5=r

Equation:-

• (x-h)²+(y-k)²=r²
• (x+2)²+(y-3)²=5²
• (x+2)²+(y-3)²=25★

More simply.

• x²+4x+4+y²-6y+9=25
• x²+y²+4x-6y=12

#2

• Centre(1,1)
• Radius=3

Equation

• (x-1)²+(y-1)²=3²
• (x-1)²+(y-1)²=9★

Answer 2

Explanation:

• Center: (h, k) (the coordinate of the middle point)
• r(radius): d(diameter)/2 (can be found by counting the number of units vertically or horizontally)
• Standard form of a circle: (x - h)² + (y - k)² = r²

1.

Center: (-2, 3)

Radius: 10/2 = 5

Standard form/ equation: (x + 2)² + (y - 3)² = 25

Standard form:

(x - (-2))² + (y - 3)² = 5²

(x + 2)² + (y - 3)² = 25

2.

Center: (1, 1)

Radius: 6/2 = 3

Standard form/ equation: (x - 1)² + (y - 1)² = 9

Standard form:

(x - 1)² + (y - 1)² = 3²

(x - 1)² + (y - 1)² = 9

Hope this helps!