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does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Question
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
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Mathematics
4 years
2021-08-02T07:43:07+00:00
2021-08-02T07:43:07+00:00 2 Answers
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Answers ( )
Given equation of the Circle is ,
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle.
Answer:
The equation of the given circle is x
2
+y
2
=25
⇒ Centre =(0,0) and radius =5
Distance between point (−2.5,3.5) and centre (0,0)
=
(−2.5−0)
2
+(3.5−0)
2
=
6.25+12.25
=
18.5
=4.3(approx)<5
Since the distance between point (−2.5,3.5) and centre (0,0) of the circle is less than the radius of the circle.
Hence the point (−2.5,3.5) lies inside the circle.