Inside a parabola

A triangle of area 64 square units is drawn inside the parabola $y=k^2-x^2$. Find the value of $k$.
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



The points where the parabola $y=k^2-x^2$ crosses the coordinate axes are joined to form a triangle.

Image
Inside a Parabola
 

The area of the triangle is 64 square units. What is the value of $k$?

This problem is adapted from the World Mathematics Championships