Statement 1 : An equation of a common tangent to the parabola y 2 = 16 3 x and the ellipse 2 x 2 + y 2 = 4 is y = 2 x + 2 3 . Statement 2 : If the line y = m x + m 4 3 , ( m  = 0 ) is a commo

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Statement 1 : An equation of a common tangent to the parabola y 2 = 16 3 ​ x and the ellipse 2 x 2 + y 2 = 4 is y = 2 x + 2 3 ​ . Statement 2 : If the line y = m x + m 4 3 ​ ​ , ( m  = 0 ) is a common tangent to the parabola y 2 = 16 3 ​ x and the ellipse 2 x 2 + y 2 = 4 , then m satisfies m 4 + 2 m 2 = 24 .

TestHub · Accepted Answer

y 2 = 16 3 ​ x 2 x 2 ​ + 4 y 2 ​ = 1 y = m x + m 4 3 ​ ​ is tangent to parabola which is tangent to ellipse ⇒ c 2 = a 2 m 2 + b 2 ⇒ m 2 48 ​ = 2 m 2 + 4 ⇒ m 4 + 2 m 2 = 24 ⇒ m 2 = 4

Mathematics - Parabola Question with Solution | TestHub

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