# Find Points Of Intersection of Ellipse and Line - Calculator

A calculator to find the points of intersection of a ellipse and a line.

## Intersection of Ellipse and Line

The equation of the ellipse is of the form**(x - h)**

^{2}/ a^{2}+ (y - k)^{2}/ b^{2}= 1**y = m x + B**

^{2}/ a

^{2}+ (y - k)

^{2}/ b

^{2}= 1, we end up with a quadratic equation given by:

^{2}/ a

^{2}+ (m x + B - k)

^{2}/ b

^{2}= 1

which may be rearranged as a quadratic equation written as

(b

^{2}+ a

^{2}m

^{2}) x

^{2}+ (-2 h b

^{2}+ 2 m a

^{2}B - 2 m a

^{2}k) x + (b

^{2}h

^{2}+ a

^{2}k

^{2}+ a

^{2}B

^{2}- 2 a

^{2}B k - a

^{2}b

^{2}) = 0

To find the points of intersection, this calculator solves the above equation to find the x coordinates and then uses equation y = m x + B to find the y coordinates.

## Use Calculator to Find Points Of Intersection of Ellipse and Line

1 - Enter the coordinates (h , k) of the center of the ellipse and the constant a and b then enter the slope m of the line and its y intercept B; then press "Calculate". The x and y coordinates of the two points of intersection P1 and P2 are displayed.Note that this problem may have two points of intersection, one point of intersection or no points of intersection.

### More References and links

Find the Points of Intersection of a Parabola with a Line . Another tutorial on finding the points of intersection of a parabola with a line; general analytical solution.ellipse

line

Maths Calculators and Solvers .