The ellipse x 2 + 4 y 2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point ( 4 , 0 ) . Then the equation of t

Question

The ellipse x 2 + 4 y 2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point ( 4 , 0 ) . Then the equation of the ellipse is

TestHub · Accepted Answer

x 2 + 4 y 2 = 4 ⇒ 4 x 2 ​ + 1 y 2 ​ = 1 ⇒ a = 2 , b = 1 ⇒ P = ( 2 , 1 ) Required Ellipse is a 2 x 2 ​ + b 2 y 2 ​ = 1 ⇒ 4 2 x 2 ​ + b 2 y 2 ​ = 1 ( 2 , 1 ) lies on it ​ ⇒ 16 4 ​ + b 2 1 ​ = 1 ⇒ b 2 1 ​ = 1 − 4 1 ​ = 4 3 ​ ⇒ b 2 = 3 4 ​ ∴ 16 x 2 ​ + ( 3 4 ​ ) y 2 ​ = 1 ⇒ 16 x 2 ​ + 4 3 y 2 ​ = 1 ⇒ x 2 + 12 y 2 = 16 ​

Mathematics - Ellipse Question with Solution | TestHub

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