Gujarat 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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