# 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}/ a^{2}- (y - k)^{2}/ b^{2}= 1and the equation of the line is of the slope intercept form

**y = m x + B**

If 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 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.

### More References and links

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.Maths Calculators and Solvers .