How do I factor this with the 2x^2 ?

Find the center ( h,k ) and the radius of the circle 2x^2 + 10x +2y^2 + y - 8 = 0

1 Answer
Oct 28, 2016

centre is (-5/2, -1/4)(52,14)

radius r=sqrt(165/16)=sqrt165/4r=16516=1654

Explanation:

2x^2+10x+2y^2+y-8=02x2+10x+2y2+y8=0

to find centre of the circle we need to complete the squares on the x & y parts of the equation.

When completing the square get the coefficient of the square terms =1

Divide everything by 2 to begin with.

x^2+5x+y^2+y/2-4=0x2+5x+y2+y24=0

(x^2+5x)+(y^2+y/2)-4=0(x2+5x)+(y2+y2)4=0

(x^2+5x+(5/2)^2)+(y^2+y/2+(1/4)^2)-4-(5/2)^2-(1/4)^"=0(x2+5x+(52)2)+(y2+y2+(14)2)4(52)2(14)=0

(x+5/2)^2+(y+1/4)^2-4-25/4-1/16=0(x+52)2+(y+14)24254116=0

(x+5/2)^2+(y+1/4)^2=165/16(x+52)2+(y+14)2=16516

cmp (x-a)^2+(y-b)^2=r^2(xa)2+(yb)2=r2

centre is (-5/2, -1/4)(52,14)

radius r=sqrt(165/16)=sqrt165/4r=16516=1654