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NCERT Class XI Mathematics - Conic Sections - Solutions

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Question : 15 of 71
Marks: +1, -0
Does the point (–2.5, 3.5) lie inside, outside or on the circle x2+y2x^2 + y^2 = 25?
Solution:  
The equation of given circle is x2+y2x^2 + y^2 = 25
(x0)2+(y0)2(x-0)^2 + (y-0)^2 = (5)2(5)^2
Comparing it with (xh)2+(yk)2(x-h)^2 + (y-k)^2 = r2r^2, we get h = 0, k = 0, and r = 5
Now, distance of the point (–2.5, 3.5) from the centre (0, 0)
= (0+2.5)2+(03.5)2\sqrt{(0+2.5)^2+(0-3.5)^2} = 6.25+12.25\sqrt{6.25+12.25} = 18.5\sqrt{18.5} = 4.3 < 5
$Thus the point (–2.5, 3.5) lies inside the circle.
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