How do you write the equation in standard form x2+y2−4x−14y+29=0?

1 Answer
George C.
Dec 1, 2015

Complete the square for x and y to find:

(x−2)2+(y−7)2=24

or if you prefer:

(x−2)2+(y−7)2=(√24)2

which is in standard (x−h)2+(y−k)2=r2 form.

Explanation:

0=x2+y2−4x−14y+29

=(x2−4x+4)+(y2−14y+49)+(29−4−49)

=(x−2)2+(y−7)2−24

Add 24 to both ends to get:

(x−2)2+(y−7)2=24

This is the equation of a circle with centre (2,7) and radius √24=2√6

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