Question

Match the description of each circle to the equation of the circle

Answer 1

we have to match the description of each circle to the equation of the circle.

solution : If (a, b) is the centre of circle and r is the radius of the circle then equation of circle is given by, (x - a)² + (x - b)² = r²

1. A circle with centre on (7,0) with a radius 9.

equation : (x - 7)² + (y - 0)² = 9²

⇒(x - 7)² + y² = 81

2. A circle with centre on the origin and point on (4, -2).

so the radius of circle, r = √{(4)² + (-2)²} = √20

Therefore equation : (x - 0)² + (y - 0)² = (√20)² = 20

⇒x² + y² = 20

3. A circle with centre (-3,-3) with a point on (-3, -2)

so the radius of circle, r = √{(-3+3)² + (-3+2)²} = 1

therefore equation : (x + 3)² + (y + 3)² = 1²

⇒(x + 3)² + (y + 3)² = 1

4. A circle with centre (0, -2) and a radius of 9.

the equation : (x - 0)² + (y + 2)² = 9²

⇒x² + (y + 2)² = 81