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Graphical Representation of Quadratic Equation

State whether...

Question

State whether the given statement is True or False. The point $(1, 2)$ lies inside the circle $x^{2} + y^{2} - 2 x + 6 y + 1 = 0.$

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Solution

We have point $(1, 2)$ and circle
$x^{2} + y^{2} - 2 x + 6 y + 1 = 0$ .
Let $S_{=} x^{2} + y^{2} - 2 x + 6 y + 1 \dots (1)$
Substitute $x = 1, y = 2$ in equation $(1)$
$\Rightarrow S_{1} = 1 + 4 - 2 \times 1 + 6 \times 2 + 1$
$\Rightarrow S_{1} = 16 > 0$

Thus, the point lies outside the circle.

Hence, statement is false.

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