Intersection of Ellipse and LineThe equation of the ellipse is of the form
(x - h)2 / a2 + (m x + B - k)2 / b2 = 1
which may be rearranged as a quadratic equation given by
(b2 + a2 m2) x2 + (-2 h b2 + 2 m a2 B - 2 m a2 k) x + (b2 h2 + a2 k2 + a2 B2 - 2 a2 B k - a2 b2) = 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 Line1 - 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.