JEE Advanced 2013 Mathematics question
A line L : y = mx + 3 meets y-axis at E(0, 3) and the arc of the parabola , at the point . The tangent to the parabola at intersects the y-axis at . The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum. Match List I with List II and select the correct answer using the code given below the lists : List I P. m = Q. Maximum area of ΔEFG is R. = S. = List II 1. 2. 4 3. 2 4. 1
Answer: (A)
Solution
Take with , i.e. . The tangent at F is , meeting the y-axis at . Triangle EFG has base EG on the y-axis and height : area \dfrac4t)(4t^2)$
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