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Conic Sections — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsConic Sections1 Mark
Question
State Whether the statements are True or False. Justify.
The point $(1, 2)$ lies inside the circle $x^2 + y^2 - 2x + 6y + 1 = 0.$
✓

Answer

False.
Solution:
Given equation of circle is $x^2 + y^2 - 2x + 6y + 1 = 0$
Here $2g = -2 \Rightarrow g = -1 2f = 6 \Rightarrow f = 3$
$\therefore$ Centre $= (-g, -f) = (1, -3)$ and
$\text{r}=\sqrt{\text{g}^2+\text{f}^2-\text{c}}=\sqrt{1+9-1}=3$
$\therefore$ Distance between the point lies outside the circle.
 Hence, the given statement is False.

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