Find all the points on the ellipse 3x^2-xy+y^2=64 that lie on the line y=3x

Answer 1

put for y, 3x into the equation.

3x^2-x*3x + 9x^2=64
9x^2=64

x= +- sqrt (64/9) you can reduce this

and y is +-3sqrt (64/9) you can reduce this.