What is the radius of the circle x^2 + 8x + y^2 - 16y + 12 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The radius of the circle x^2 + 8x + y^2 - 16y + 12 = 0 has to be determined.

x^2 + 8x + y^2 - 16y + 12 = 0

=> x^2 + 8x + 16 + y^2 - 16y + 64 = -12 + 16 + 64

=> (x + 4)^2 + (y - 8)^2 = 68

This is the general form of the equation of a circle with center (h, k) and radius r: (x - h)^2+ (y - k)^2 = r^2

The radius of (x + 4)^2 + (y - 8)^2 = 68 is `sqrt 68`

The radius of the circle x^2 + 8x + y^2 - 16y + 12 = 0 is `sqrt 68`

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heba1986 | Teacher | (Level 1) eNoter

Posted on

if we want to know the radious of circle you should change the equation of circle to the general form

the  general form is :

(x-a)^2+(y-b)^2=r^2

the radious is r

=>x^2+8x+(8/2)^2-(8/2)^2+y^2-16y+(16/2)^2-(16/2)^2+12=0

x^2+8x+16+y^2-16y+64=16+64-12

(x+4)^2+(y-8)^2=68

=>the radious of the circle is r=sqrt 68

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