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If the circle...

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If the circle x2+y2-4x-8y+16=0 rolls up the †an gent to it at (2+\sqrt{3 },3) by 2 units (assumes x-axis as horizontal) , then the centre of the circle in the position i

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x^{2} + y^{2} - 4 x - 8 y + 16 = 0

rolls up the tangent to it at

(2 + \sqrt{3}, 3)

2

units, assuming the x-axis as horizontal, the equation of the circle in the new position is

Q. Find the equation of tangent to the circle

x^{2} + y^{2} - 4 x - 8 y + 16 = 0

(2 + \sqrt{3}, 3)

. If the circle rolls up along this tangent by

2

units then find its equation in the new position.

Q. If the circle

x^{2} + y^{2} - 4 x - 8 y + 16 = 0

rolls up (away from

x -

axis) along the tangent to it at

(2 + \sqrt{3}, 3)

2

units and its equation in the new position is

x^{2} + y^{2} + 2 a x + 2 b y + c = 0,

then the value of

a^{2} + 8 b + c

Q. The equation of the circle which is touched by

y = x

, has its centre on the positive direction of the

x

-axis and cuts off a chord of length

2

units along the line

\sqrt{3} y - x = 0

Q. A circle is drawn with y-axis as a tangent and its centre at the point which is the reflection of (3, 4) in the line y = x. The equation of the circle is

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