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Find the equation of a circle, in standard form, with endpoints a center at (2,-1) and a radius of 4

User Val Berthe
by
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1 Answer

7 votes

(x+2)2+(y−1)2=10

Step-by-step explanation:

The simplest equation for a circle is:

XXX2+Y2=R2

for a circle with center at (0,0) R

and radius

If we want to shift this so the center is at

(−2,1)

then the

X

values become x=X−2xx→xxX=x+2

and the Y values become yy=Y−1xx → xxY=y−1=Y−1xx→xxY=y−1 So X 2+Y becomes

(x+2)2+(y−1)2

The radius is unaffected by the shift and will remain the same length.

The radius is the distance between the center

(−2,1)

and any point on the circumference; in this case we are given the point

(1,0)

Using the Pythagorean Theorem this gives us a radius squared of

XXXR2=((−2)−1)2+(1−0)2=10

Therefore the equation of our (shifted) circle will be

XXX(x+2)2+(y−1)2=10

User Napoli
by
8.8k points

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