35.answerx^2+y^2-8x+12=0explanationcenter 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 = 2unitsgeneral equation of a circle is given by;(x-h)^2+(y-k)^2=r^2where (h,k) is center and r is radius:(x-4)^2+(y-0)^2=2^2expanding the equationx(x-4)-4(x-4)+y(y-0)-0(y-0)=4x^2-4x-4x+16+y^2-0-0+0=4collecting like termsx^2-8x+y^2+16-4=0x^2+y^2-8x+12=036.answerx^2+y^2-16x-12y+64=0explanationcenter=(8,6)point (g,f)= (8,12)radius=√[(8-8)^2+(12-6)^2]radius=6unitssubstitution into;(x-h)^2+(y-k)^2=r^2(x-8)^2+(y-6)^3=6^2x(x-8)-8(x-8)+y(y-6)-6(y-6)=36x^2-8x-8x+64+y^2-6y-6y+36=36x^2-16x+y^2-12y+100=36x^2+y^2-16x-12y+64=0