Co-ordinate Geometry

Question

A student has drawn accurately the hyperbola y=12/x. What straight line must be drawn to meet this hyperbola, so that the x-coordinates of their points of intersection would solve x²+4x-12=0.

Answer 1

x^2 + 4x - 12 = 0

(x + 6)(x - 2 ) = 0

x+6=0 or x-2= 0

x = -6 and x=2

y = 12/-6 = -2

y = 12/2 = 6

(-6,-2) and (2,6)