toxicsugar22
  • toxicsugar22
4x^2-6y^2+32x-24y+16=0 give the exact coordinated of an four points
Mathematics
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chestercat
  • chestercat
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anonymous
  • 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 \(y=-2/3(3-\sqrt5)\).
anonymous
  • 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 \(x=-2(2-\sqrt{3})\).
toxicsugar22
  • toxicsugar22
so what aret the points

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toxicsugar22
  • toxicsugar22
what are the points
toxicsugar22
  • toxicsugar22
can u help me
anonymous
  • anonymous
(0,-2/3(3+sqrt5), (0,-2/3(3-sqrt5), (-2(2+sqrt3),0), (-2(2-sqrt3),0)
toxicsugar22
  • toxicsugar22
thanks can u help me with one more
toxicsugar22
  • toxicsugar22
12x^2-3y^2+24y-84=0 give the exact coordinates of any four points on the hyperbola

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