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Equations of a Circle
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Q1
Find the equation of the circle with centre (1, 1) and radius2.
Marks:2Answer:

Q2
Find the equation of the circle whose radius is 4 units and which is concentric with the circle
x^{2} + y^{2} + 2x – 6y = 0
Marks:1Answer:
x^{2} + y^{2} +2x – 6y = 0
Here, 2g = 2 , 2f = – 6
g = 1, and f = – 3
The coordinates 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} = 4^{2}
x^{2} + 2x + 1 + y^{2} – 6y + 9 = 16
x^{2} + y^{2} +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:1Answer:
The equation of the circle which has A(x_{1, }y_{1}) and B(x_{2}, y_{2}) as the opposite ends of a diameter is
(x – x_{1})(x– x_{2}) + (y– y_{1})(y– y_{2}) = 0
or, (x– 1)(x– 4) + (y– 3)(y– 5) = 0
or, x^{2} – 5x + 4 + y^{2} – 8y + 15 = 0
x^{2} + y^{2} – 5x – 8y + 19 = 0

Q4
Find the equation of circle having centre at origin and radius unity.
Marks:1Answer:

Q5
Find the centre and radius of the circle
(x 3)^{2} + (y – 2)^{2} = 25.Marks:1Answer:
The equation of circle is
(x 3)^{2} + (y – 2)^{2} = (5)^{2}
centre is (3,2) and radius, r = 5.