NTA Abhyas JEE Main2020MathematicsEllipsePractice

If y = x + c touches the ellipse 3 x 2 + 4 y 2 = 12 at the point P , then the value of the length O P (where O is the origin) is equal to

Options

A3 units
B7 units
C5 7 units
D7 5 units

Correct answer

C. 5 7 units

Step-by-step solution

If y = x + c touches x 2 4 + y 2 3 = 1 then, c = ± 4 1 + 3 = ± 7 Let's assume, c = 7 and y = x + 7 touches x 2 4 + y 2 3 = 1 at h , k . then, x h 4 + y k 3 = 1 is same as y - x = 7 ⇒ h 4 - 1 = k 3 1 = 1 7 ⇒ h , k = - 4 7 , 3 7 = P Hence, O P = 16 7 + 9 7 = 5 7 units

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