Bizarre Hyperbola

Calculus Level 4

The hyperbola above has equation \(2x^2 + 10xy + 8y^2 + 4x + 2y + 1 = 0\).

Let \(m_{1}\) and \(m_{2}\) be the slopes of the asymptotes (shown in green) such that \(|m_{1}| > |m_{2}| \), and let \(m_{3}\) be the slope of the line that passes through both points, where the tangents have infinite slopes.

Find the value of \(\dfrac{1}{|m_{1}| - |m_{2}| - |m_{3}|}\).

×

Problem Loading...

Note Loading...

Set Loading...