NTA Abhyas JEE Main2020MathematicsEllipsePractice

The length of the minor axis of the ellipse 5 x - 10 2 + 5 y + 15 2 = 3 x - 4 y + 7 2 4 is

Options

A10 3 units
B10 3 units
C20 3 units
D5 3 units

Correct answer

D. 5 3 units

Step-by-step solution

x - 2 2 + y + 3 2 = 1 2 3 x - 4 y + 7 5 2 is an ellipse, whose focus is 2 , - 3 , directix 3 x - 4 y + 7 = 0 and eccentricity is 1 2 Length of ⊥ from focus to directrix is 3 × 2 - 4 × - 3 + 7 5 = 5 a e - a e = 5 ⇒ 2 a - a 2 = 5 ⇒ a = 10 3 So, length of major axis is 20 3 and length of minor axis, b = 5 3

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