Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSConic Sections2 Marks
Question
Does the point (-2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25?
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Answer
The equation of given circle is x2 + y2 = 25 $\Rightarrow$ (x - 0)2 + (y - 0)2 = (5)2 Comparing it with (x - h)2 + (y - k)2 = r2, 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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