Given the co-ordinates (x,y) of a center of a circle and it's radius. determine whether a point lies inside the circle or outside the circle? Tell three formlaes which are used in this question?
2 answers
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The equation of a circle with given centre (x0,y0) and radius r is given by:
(x-x0)²+(y-y0)²=r²
implicitly, this equations makes use of the equation of distance between two points (x,y) and (x0,y0):
Distance = sqrt((x-x0)²+(y-y0)²)
If the distance from the centre is greater than r, then it is outside the circle. If the distance is less than r, then it is inside the circle.
I.e.
Point P1(x1,y1) is outside, on, or inside the circle if
(x1-x0)²+(y1-y0)²
is greater than, equal to, or less than
r².
(x-x0)²+(y-y0)²=r²
implicitly, this equations makes use of the equation of distance between two points (x,y) and (x0,y0):
Distance = sqrt((x-x0)²+(y-y0)²)
If the distance from the centre is greater than r, then it is outside the circle. If the distance is less than r, then it is inside the circle.
I.e.
Point P1(x1,y1) is outside, on, or inside the circle if
(x1-x0)²+(y1-y0)²
is greater than, equal to, or less than
r².
2 answers