A calculator to find the points of intersection of a hyperbola and a line. ## Intersection of a Hyperbola and LineThe equation of the the hyperbola with horizontal axis is of the form(x - h)^{2} / a^{2} - (y - k)^{2} / b^{2} = 1and the equation of the line is of the slope intercept form y = m x + BIf y = m x + B is substituted into ^{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 rewritten in standard form 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.
## How to Use the Calculator1 - 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. |

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