Binomial Theorem

Question
CBSEENMA11015086

Does the point (-2.5, 3.5) lie inside, outside or on the circle straight x squared plus straight y squared equals 25?

Solution

The equation of circle is straight x squared plus straight y squared equals 25
rightwards double arrow      left parenthesis straight x minus 0 right parenthesis squared plus left parenthesis straight y minus 0 right parenthesis squared space equals space 5 squared
Comparing it with the standard equation of circle, left parenthesis straight x minus straight h right parenthesis squared plus left parenthesis straight y minus straight k right parenthesis squared equals straight r squared comma we have
h = 0, k=0 and r = 5
∴ Centre of circle is O (0, 0) radius = 5
Distance of point A (-2.5, 3.5) or straight A space open parentheses negative 5 over 2 comma space 7 over 2 close parentheses from the centre is OA space equals space square root of open parentheses 0 plus 5 over 2 close parentheses squared plus open parentheses 0 minus 7 over 2 close parentheses squared end root
                                          space space space equals square root of 25 over 4 plus 49 over 4 end root space equals space fraction numerator square root of 74 over denominator 2 end fraction less than 5
rightwards double arrow Distance of point from centre is less than the radius.
Hence, the point lies inside the circle.

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