# Equations of a Circle

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• Q1

Find the equation of the circle with centre (1, 1) and radius2.

Marks:2

• Q2

Find the equation of the circle whose radius is 4 units and which is concentric with the circle

x2 + y2 + 2x – 6y = 0

Marks:1

x2 + y2 +2x – 6y = 0

Here, 2g = 2 , 2f = – 6

g = 1, and f = – 3

The co-ordinates of the centre of required circle is (– 1,3) and radius is 4 units.

The equation of required circle is

(x +1)2 + (y – 3)2 = 42

x2 + 2x + 1 + y2 ­– 6y + 9 = 16

x2 + y2 +2x – 6y – 6 = 0

• Q3

Find the equation of the circle which has A(1,3) and B(4,5) as the opposite ends of a diameter.

Marks:1

The equation of the circle which has A(x1, y1) and B(x2, y2) as the opposite ends of a diameter is

(x – x1)(x– x2) + (y– y1)(y– y2) = 0

or, (x– 1)(x– 4) + (y– 3)(y– 5) = 0

or, x2 – 5x + 4 + y2 ­– 8y + 15 = 0

x2 + y2 – 5x – 8y + 19 = 0

• Q4

Find the equation of circle having centre at origin and radius unity.

Marks:1

• Q5

Find the centre and radius of the circle
(x -3)2 + (y – 2)2 = 25.

Marks:1