equations of circle

a
i) Find the distance of P to the line L

Ans:
Distance =
abs(0-2)/(1^2+1^2)^0.5)=(2)^0.5//

ii) Find the radius of the circle C
Ans:
(QR/2)^2+(distance of P to the line L)^2=radius^2
1^2+2=radius^2
radius=(3)^0.5//

iii) Find the equation of circle C
Ans:
(x-2)^2+(y-0)^2=3
x^2+y^2-4x+1=0//

b
i) Find the equation do the family of circles passing through Q and R

the equation do the family of circles passing through Q and R is
(x^2+y^2-4x+1)+k(x-y)=0
x^2+y^2+(k-4)x-y+1=0//

ii) Find the equation of the circle C' passing through P,Q and R

Ans:
sub P(2.0) into x^2+y^2+(k-4)x-y+1=0//
2^2+0^2+(k-4)2-0+1=0
k=5/2//

so the the equation of the circle C' passing through P,Q and R
is x^2+y^2+(3/2)x-y+1=0//

c) Show that the tangent to the circle C' at P is parallel to QR.
x^2+y^2+(3/2)x-y+1=0
2x+2y(dy/dx)+(3/2)-(dy/dx)=0
dy/dx=(4x+3)/(2-4y)

the sloer of tangent to the circle C' at P=(4(2)+3)/(2-4(0)=11/2,