## Chapter 24 – The Circle Exercise Ex. 24.1

If the lines 2x-3y = 5 and 3x-4y = 7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.

Find the equation of the circle having (1, -2) as its centre and passing through the intersection of the lines 3x + y = 14 and 2x +5y = 18.

If the lines 3x-4y+4 = 0 and 6x-8y-7 = 0 are tangents to a circle, then find the radius of the circle.

The circle x^{2}+y^{2}-2x-2y+1 = 0 is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in new-position.

## Chapter 24 – The Circle Exercise Ex. 24.2

Find the equation of the circle which circumscribes the

triangle formed by the lines.

iv. y = x + 2, 3y = 4x and 2y

= 3x.

If a circle passes through the point (0, 0), (a, 0), (0, b), then find the coordinates of its centre.

Find the equation of the circle which passes through

the point (2, 3) and (4, 5) and the centre lies on the straight line y – 4x +

3 = 0.

## Chapter 24 – The Circle Exercise Ex. 24.3

ABCD is a square whose side is a; taking AB and AD as

axes, prove that the equation of the circle circumscribing the square is x^{2}

+ y^{2} – a (x + y) = 0

## Chapter 24 – The Circle Exercise Ex. 24VSAQ