1.

Find the equation of an ellipse whose foci are (-3,5) and (5,5) and major axis is 10​

Answer»

the equation of an ellipse WHOSE FOCI are (-3,5) and (5,5) and major AXIS is 10​ is  \dfrac{(x-1)^2}{25} + \dfrac{(y-5)^2}{9}

  • Given,
  • 2a = 10 ⇒ ∴ a = 5
  • standard FORM equation of ellipse is:
  • \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2}=1
  • foci (-3,5) and (5,5)
  • mid-point is given by,  \dfrac{-3+5}{2}, \dfrac{5+5}{2} = (1, 5)
  • ∴ (1, 5) is the mid-point.
  • Now, x = X+1, y = Y+5
  • ⇒ x = ae + 1, y = 0+5
  • ⇒ (ae+1, 5)
  • ae+1 = 5
  • ae = 4
  • E = 4/a = 4/5
  • ∴ e = 4/5
  • e^2 = 1 - b^2/a^2
  • 4^2/5^2 = 1- b^2/5^2
  • 4^2 = 5^2-b^2
  • b^2 = 3^2
  • ∴ b =3
  • Therefore the equation of an ellipse is given by,
  • \dfrac{(x-1)^2}{25} + \dfrac{(y-5)^2}{9}


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