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Question

The area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latusrectum is
(a) 12 sq. units
(b) 16 sq. units
(c) 18 sq. units
(d) 24 sq. units

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Solution

The given equation of parabola is
x2 = 12y ...(1)
which is of the form x2 = 40y --(2)
∴ comparing (1) and (2),
we get 12y = 40y
i.e. a = 3

Let P be the focus for parabola,
i.e. OP = 3
Length of lotus rectum is 4a
= 4 × 3
= 12
Area of triangle AOB= 12 × Base × Altitude= 12 × AB × OP= 12 × 12 × 3
i.e. Area of triangle formed = 18 square units.

Hence, the correct answer is option C.

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