Find the center of the circle $x^{2} + y^{2} - 6 x + 4 y - 23 = 0$ .

(3, - 2)

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(3, 2)

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(- 3, 2)

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(- 3, - 2)

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none of these

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Solution

The correct option is A $(3, - 2)$
Equation of the circle is
$x^{2} + y^{2} - 6 x + 4 y - 23 = 0$
$=> x^{2} - 6 x + y^{2} + 4 y - 23 = 0$
$=> x^{2} - 2.3. x + 3^{2} + y^{2} + 2. y .2 + 2^{2} = 23 + 3^{2} + 2^{2}$
$=> (x - 3)^{2} + (y + 2)^{2} = 23 + 9 + 4$
$∴$ Centre of circle is $(3, - 2)$

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Find the center of the circle x2+y2−6x+4y−23=0.

The correct option is A (3,−2)Equation of the circle isx2+y2−6x+4y−23=0=>x2−6x+y2+4y−23=0=>x2−2.3.x+32+y2+2.y.2+22=23+32+22=>(x−3)2+(y+2)2=23+9+4∴ Centre of circle is (3,−2)

Find the center of the circle $x^{2} + y^{2} - 6 x + 4 y - 23 = 0$ .

The correct option is A $(3, - 2)$
Equation of the circle is
$x^{2} + y^{2} - 6 x + 4 y - 23 = 0$
$=> x^{2} - 6 x + y^{2} + 4 y - 23 = 0$
$=> x^{2} - 2.3. x + 3^{2} + y^{2} + 2. y .2 + 2^{2} = 23 + 3^{2} + 2^{2}$
$=> (x - 3)^{2} + (y + 2)^{2} = 23 + 9 + 4$
$∴$ Centre of circle is $(3, - 2)$