What is the equation of the circle with a center at (4 ,-1 )(4,−1) and a radius of 8 8?

2 Answers
sjc
Jun 25, 2018

x^2+y^2-8x+2y-47=0x2+y2−8x+2y−47=0

Explanation:

the eqn of a circle centre (a,b)(a,b) and radius rr

(x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2

#we ahve

(x-4)^2+(y- -1)^2=8^2(x−4)2+(y−−1)2=82

(x-4)^2+(y+1)^2=64(x−4)2+(y+1)2=64

x^2-8x+16+y^2+2y+1=64x2−8x+16+y2+2y+1=64

x^2+y^2-8x+2y-47=0x2+y2−8x+2y−47=0

Jim G.
Jun 25, 2018

(x-4)^2+(y+1)^2=64(x−4)2+(y+1)2=64

Explanation:

"the equation of a circle in standard form is"the equation of a circle in standard form is

color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))

"where "(a,b)" are the coordinates of the centre and r"
"is the radius"

"here "(a,b)=(4,-1)" and "r=8

(x-4)^2+(y-(-1))^2=8^2

(x-4)^2+(y+1)^2=64larrcolor(red)"equation of circle"

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