If a and c are positive real numbers and the ellipse 4 c 2 x 2 + c 2 y 2 = 1 has four distinct points ir common with the circle x 2 + y 2 = 9 a 2 , then

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If a and c are positive real numbers and the ellipse 4 c 2 x 2 ​ + c 2 y 2 ​ = 1 has four distinct points ir common with the circle x 2 + y 2 = 9 a 2 , then

TestHub · Accepted Answer

Radius = 3 a Length of major axis = 4 c Now, (Radius ) < (Half of the length of major axis) 3 a < 2 c 9 a 2 < 4 c 2 9 a c − 9 a 2 > 9 a c − 4 c 2 9 a c − 9 a 2 − 2 c 2 > 9 a c − 6 c 2 Again 3 a < 2 c ⇒ 9 a c < 6 c 2 ⇒ 9 a c − 6 c 2 < 0 From (i) and (ii), 9 a c − 9 a 2 − 2 c 2 > 0

Mathematics - Ellipse Question with Solution | TestHub

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