the district of a point from center must be great /less compare to radius for point to be exterior to the circle
Answers
To determine the position of a given point with respect to a circle, all we need to do is to find the distance between the point and the center of the circle, and compare it with the circle’s radius.
If the distance is greater than the radius, the point lies outside. If it’s equal to the radius, the point lies on the circle. And if it’s less than the radius, you guessed it right, the point will lie inside the circle. As simple as that!
To establish some formulas, let’s take the standard equation first i.e. x2 + y2 – r2 = 0.
Let P(x1, y1) be the point whose position is to be determined. Then it’s distance from the center of the circle C(0, 0) will be given by
CP = x12+y12−−−−−−−−√
Now, the point will lie outside, on or inside the circle when CP > r, CP = r or CP < r respectively. By rearrangement of terms, we get the required conditions as
Outside: x12 + y12 – r2 > 0
On: x12 + y12 – r2 = 0
Inside: x12 + y12 – r2 < 0
This is equivalent to substituting the coordinates of the point in the circle’s equation, and checking its sign.
If the resulting expression is positive, then the point lies outside circle, if zero, then on the circle, and if negative then inside the circle. Neat.
Now let’s move on to the general equation: x2 + y2 + 2gx + 2fy + c = 0.
Answer:
nee adhala nakinkathelupettu