Given an ellipse centered at (h, k), with semi-major axis a, semi-minor axis b, both aligned with the Cartesian plane. The task is to determine if the point (x, y) is within the area bounded by the ellipse.
Input: h = 0, k = 0, x = 2, y = 1, a = 4, b = 5 Output: Inside Input: h = 1, k = 2, x = 200, y = 100, a = 6, b = 5 Output: Outside
Approach: We have to solve the equation of ellipse for the given point (x, y),
(x-h)^2/a^2 + (y-k)^2/b^2 <= 1
If in the inequation, results comes less than 1 then the point lies within, else if it comes exact 1 then the point lies on the ellipse, and if the inequation is unsatisfied then point lies outside of the ellipse.
Below is the implementation of the above approach:
- Check if a point is inside, outside or on the parabola
- How to check if a given point lies inside or outside a polygon?
- Check whether a given point lies inside a rectangle or not
- Check whether a point lies inside a sphere or not
- Check whether a given point lies inside a triangle or not
- Check whether a given point lies on or inside the rectangle | Set 3
- Check if a point lies on or inside a rectangle | Set-2
- Triangle with no point inside
- Find if a point lies inside a Circle
- Find a point that lies inside exactly K given squares
- Find intersection point of lines inside a section
- Find minimum radius such that atleast k point lie inside the circle
- Check if a given circle lies completely inside the ring formed by two concentric circles
- Check whether the point (x, y) lies on a given line
- Check whether given floating point number is even or odd
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