Find the coordinates of the center of a circle whose equation is $x^{2} + y^{2} - 4 x 2 y = 75$ .

(4, 1)

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(1, 4)

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(2, 1)

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(1, 2)

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(3, 1)

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Solution

The correct option is C $(2, 1)$
Given equation of circle is $x^{2} + y^{2} - 4 x - 2 y = 75$
$\Rightarrow {(x - 2)}^{2} + {(y - 1)}^{2} = 80$
$\Rightarrow x^{2} - 4 x + 4 + y^{2} - 2 y + 1 = 75$
$\Rightarrow (x - 2)^{2} + (y - 1)^{2} = 75$
Therefore the coordinates of the center of circle is $(2, 1)$ .

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Find the coordinates of the center of a circle whose equation is x2+y2−4x2y=75.

The correct option is C (2,1)Given equation of circle is x2+y2−4x−2y=75⇒(x−2)2+(y−1)2=80⇒x2−4x+4+y2−2y+1=75⇒(x−2)2+(y−1)2=75Therefore the coordinates of the center of circle is (2,1).

Find the coordinates of the center of a circle whose equation is $x^{2} + y^{2} - 4 x 2 y = 75$ .