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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. - Mathematics

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Question

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 parabola is x2 = 12y.

On comparing this equation with x2 = 4ay, we obtain 4a = 12 ⇒ a = 3

∴The coordinates of foci are S (0, a) = S (0, 3)

Let AB be the latus rectum of the given parabola.

The given parabola can be roughly drawn as

At y = 3, x2 = 12 (3) ⇒ x2 = 36 ⇒ x = ±6

∴The coordinates of A are (–6, 3), while the coordinates of B are (6, 3).

Therefore, the vertices of ΔOAB are O (0, 0), A (–6, 3), and B (6, 3).

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Solution 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. Concept: Parabola - Latus Rectum.
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