Question

A point p moves such thay the tangents pt1 and pt2 from it to hyperbola 4x^2-9y^2=36 are mutually perpendicular. Find locus of p

Answer 1

First put the equation into the form (x-h)²/a² - (y-k)²/b² = 1.  

4x² - 9y² = 36  

x²/9 - y²/4 = 1  

x²/3² - y²/2² = 1  

This is a horizontal hyperbola centered at the origin.  

The asymptotes are y = -2/3x and y = 2/3x regardless of them being non perpendicular