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 / 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. |