NCERT Class XI Mathematics - Conic Sections - Solutions

Question : 68

Total: 71

Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.

Solution:

The given equation of parabola is x2 = 12y, which is of the form x2 = 4ay.

∴ 4a = 12 ⇒ a = 3
Focus of the parabola is (0, 3)
Let AB be the latus rectum of the parabola then, equation of AB is y = 3
∴ x2 = 4 × 3 × 3 = 36 ⇒ x = ±6
The coordinates of A are (–6, 3) and B are (6, 3)
∴ Area of ΔOAB
=

|0 (3 - 3) - 6 (3 - 0) + 6 (0 - 3)| =

|- 36| = 18 sq. units.

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