CBSE BoardEnglish MediumSTD 11 ScienceMathsConic Sections2 Marks
Question
Does the point $(-2.5, 3.5)$ lie inside, outside or on the circle $x^2 + y^2 = 25?$
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Answer
The equation of given circle is
$x^2 + y^2 = 25$
$\Rightarrow (x - 0)^2 + (y - 0)^2 = (5)^2$
Comparing it with $(x - h)^2 + (y - k)^2 = r^2,$ we have
$h = 0 , k = 0$ and $r = 5$
Now distance of the point $(-2.5, 3.5)$ from the centre $(0, 0)$
$= \sqrt {{{(0 + 2.5)}^2} + {{(0 - 3.5)}^2}} = \sqrt {6.25 + 12.25} = \sqrt {18.5} = 4.3 < 5$
Thus the point $(-2.5, 3.5)$ lies inside the circle.
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