Question

prove that the curves 3x^2-y^2=12 and x^2+3y^2-24=0 intersect at right angle at point (root 6,root6)

Answer 1

work out dy/dx at x=sqrt(6)

Answer 2

To prove this it is sufficient to prove that tangents are perpendicular at root6.root6 for this you need slope of tangent at that point which is given by dy/dx, so differentiate both,
6x-2yy'= y'=3x/y y'=3 2x+6yy'=0 hence y'=-1/3 so m1m2=-1 implies they are perpendicular.

Answer 3

check wether the slope(dy/dx) of both the graph are negative resiprocals of each other at that given point.

Answer 4

thanks