Given a parabola with vertex (h, k), and , the distance between focus and vertex. The task is to determine if the point (x, y) is inside, outside or on the parabola.
Input: h = 100, k = 500, x = 20, y = 10, a = 4 Output: Outside Input: h = 0, k = 0, x = 2, y = 1, a = 4 Output: Inside
Approach: It is very simple, we have to just solve the equation for point (x, y):
(y-k)^2 = 4a(x-h)
or, (y-k)^2 – 4a(x-h) = 0
After solving, if the result comes less than 0 then the point lies within, else if it comes exact 0 then the point lies on the parabola, and if the result is greater than 0 unsatisfied the point lies outside of the parabola.
Here we are taking a parabola whose axis of symmetry is y = k, although the approach is applicable for any parabola.
Below is the implementation of above approach:
- Check if a point is inside, outside or on the ellipse
- 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
- Check whether a point lies inside a sphere or not
- Check whether a given point lies inside a rectangle or not
- Check whether a given point lies inside a triangle or not
- How to check if a given point lies inside or outside a polygon?
- Triangle with no point inside
- Find a point that lies inside exactly K given squares
- Find if a point lies inside a Circle
- 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 given floating point number is even or odd
- Check whether the point (x, y) lies on a given line
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