Tangent to a hyperbola: Cartesian approachEdit
The Cartesian equation of the hyperbola is . Differentiating (using the technique of Implicit differentiation to simplify the process) to find the gradient:
We can then substitute this into our point-gradient form, , using the point :
- at , .
- But we know that from the definition of the hyperbola, so
Normal to a hyperbola: Cartesian approachEdit
The gradient of the normal is given by , i.e., . Finding the equation,