If $(h, k)$ is the centre of $x^{2} + y^{2} - 2 x - 4 y + 11 = 0$ , find the value of $h^{2} + k^{2} + h k$ .

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Solution

The centre of the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ is $(- g, - f)$ .
Equation of the given circle is x² + y² - 2x - 4y + 11 = 0
$\Rightarrow$ g = -1 and f = -2
$\Rightarrow$ centre $\equiv (1, 2)$

$\Rightarrow$ Answer $= 1 + 4 + 2 = 7$

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If (h,k) is the centre of x2 + y2 − 2x − 4y + 11 = 0, find the value of h2 + k2 + hk. ___

The centre of the circle x2 + y2 + 2gx + 2fy + c = 0 is (−g,−f). Equation of the given circle is x2 + y2 - 2x - 4y + 11 = 0 ⇒ g = -1 and f = -2 ⇒ centre ≡ (1,2) ⇒ Answer =1 + 4 + 2 = 7

If $(h, k)$ is the centre of $x^{2} + y^{2} - 2 x - 4 y + 11 = 0$ , find the value of $h^{2} + k^{2} + h k$ .

___

The centre of the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ is $(- g, - f)$ .
Equation of the given circle is x² + y² - 2x - 4y + 11 = 0
$\Rightarrow$ g = -1 and f = -2
$\Rightarrow$ centre $\equiv (1, 2)$

$\Rightarrow$ Answer $= 1 + 4 + 2 = 7$