# Find Points Of Intersection of a Hyperbola and Line - Calculator

A calculator to find the points of intersection of a hyperbola and a line.

## Intersection of a Hyperbola and Line

The equation of the the hyperbola with horizontal axis is of the form
(x - h)2 / a2 - (y - k)2 / b2 = 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 / a2 - (y - k)2 / b2 = 1
we end up with a quadratic equation given by:
(x - h)2 / a2 - (m x + B - k)2 / b2 = 1 which may be rewritten in standard form as
(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.

## 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.

 Hyperbola: (h , k) are the coordinates of the center of the hyperbola and a and b are constants that determine the slopes of the asymptotes. h = 1 , k = 1 a = 1 , b = 1 Line m = 1 , B = 1 Decimal places = 4 Coordinates of the points of intersection P1( , ) P2( , )