# 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 LineThe equation of the ellipse is of the form(x - h)^{2} / a^{2} + (y - k)^{2} / b^{2} = 1y = m x + B^{2} / a^{2} + (y - k)^{2} / b^{2} = 1
(x - h) ^{2} / a^{2} + (m x + B - k)^{2} / b^{2} = 1
which may be rearranged as a quadratic equation given by (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.
## How to use the calculator1 - 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 "enter". 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

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Maths Calculators and Solvers .