## toxicsugar22 5 years ago 4x^2-6y^2+32x-24y+16=0 give the exact coordinated of an four points

1. anonymous

Hello toxi, Let's take $$x=0$$, then we will have $$-6y^2-24y+16=0$$. By solving the quadratic equation we get two values for y. That's $$y=-2/3(3+\sqrt5)$$ or $$y=-2/3(3-\sqrt5)$$.

2. anonymous

Those are already two points. Other two points can be found by plugging $$y=0$$, then $$4x^2+32x+16=0$$, which gives the solutions $$x=-2(2+\sqrt{3})$$ and $$x=-2(2-\sqrt{3})$$.

3. toxicsugar22

so what aret the points

4. toxicsugar22

what are the points

5. toxicsugar22

can u help me

6. anonymous

(0,-2/3(3+sqrt5), (0,-2/3(3-sqrt5), (-2(2+sqrt3),0), (-2(2-sqrt3),0)

7. toxicsugar22

thanks can u help me with one more

8. toxicsugar22

12x^2-3y^2+24y-84=0 give the exact coordinates of any four points on the hyperbola