1.prove that the centre of a circle passing through (0,1) and touching the curve y=x² at (2,4) is (-16/5,53/10)

 

2.two circles are drawn through (a,5a) and (4a,a) touching the axis of y.prove that they intersect at an angle tan^-1 40/9

 

3.find the equation of circle which passes through (0,0) and cuts off chords of length b from the lines y=x and y= -x

ans:x²+y²+ root2 by=0 or x²+y²-root2 by=0 [by is not in the root]

 

4.show that the equation of image of circle x²+y²+16x-24y+183=0 by the line mirror 4x+7y+13=0 is x²+y²+32x+4y+235=0

 

5.a circle passes through (2,1) and the line x+2y=1 is a tangent to it at (3,-1).determine its equation.

ans:3(x²+y²)-23x-4y+35=0

 

plzzz explain the steps properly,5 points for one correct answer.