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Question

Mathematics Question on Circle

Does the point (−2.5,3.5)(-2.5, 3.5) lie inside, outside, or on the circle x2+y2=25x^2 + y^2 = 25 ?

Answer

The equation of the given circle is
x2+y2=25x^2 + y^2 = 25
⇒(x−0)2+(y−0)2=52,⇒ (x - 0)^2 + (y - 0) ^2 = 5^2 ,

which is of the form
(x−h)2+(y−k)2=r2(x - h) 2 + (y - k) 2 = r^2 ,

where h=0h = 0 , k=0k = 0, and r=5.r = 5.

∴Centre =(0,0)= (0, 0) and radius =55
Distance between point (-2.5, 3.5) and center (0, 0)
=√[(−2.5–0)2\+(−3.5–0)2]= √[(-2.5 – 0)^2 \+ (-3.5 – 0)^2]

=√(6.25+12.25)= √(6.25 + 12.25)

=√18.5= √18.5

=4.3= 4.3 [which is <5< 5]

Since, the distance between the point (−2.5,−3.5)(-2.5, -3.5) and the center (0,0)(0, 0) of the circle is less than the radius of the circle, the point (−2.5,−3.5)(-2.5, -3.5) lies inside the circle.