A calculator to find the points of intersection of a hyperbola and a line.
The equation of the the hyperbola with horizontal axis is of the form
(x  h)^{2} / a^{2}  (y  k)^{2} / b^{2} = 1
and the equation of the line is of the slope intercept form
y = m x + B
If y = m x + B is substituted into (x  h)^{2} / a^{2}  (y  k)^{2} / b^{2} = 1, we end up with a quadratic equation given by:
(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 calculator
1  Enter the coordinates (h , k) of the center of the hyperbola 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.
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.
More Math Calculators and Solvers.
