35.
answer
x^2+y^2-8x+12=0
Step-by-step explanation
center of the centre is at(4,0)
pick another point on the circles circumference=(4,2)
using the two points;(4,0) and (4,2) calculate the radius of the circle.
radius=√[(x2-x1)^2+(y2-y1)^2]
radius=√[(4-4)^2+(2-0)^2]
radius = 2units
general equation of a circle is given by;
(x-h)^2+(y-k)^2=r^2
where (h,k) is center and r is radius:
(x-4)^2+(y-0)^2=2^2
expanding the equation
x(x-4)-4(x-4)+y(y-0)-0(y-0)=4
x^2-4x-4x+16+y^2-0-0+0=4
collecting like terms
x^2-8x+y^2+16-4=0
x^2+y^2-8x+12=0
36.
answer
x^2+y^2-16x-12y+64=0
Step-by-step explanation
center=(8,6)
point (g,f)= (8,12)
radius=√[(8-8)^2+(12-6)^2]
radius=6units
substitution into;
(x-h)^2+(y-k)^2=r^2
(x-8)^2+(y-6)^3=6^2
x(x-8)-8(x-8)+y(y-6)-6(y-6)=36
x^2-8x-8x+64+y^2-6y-6y+36=36
x^2-16x+y^2-12y+100=36
x^2+y^2-16x-12y+64=0