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What is the area of the triangle formed by the lines joining the vertex of the parabola x2 = 20y to the end of the latus rectum?

What is the area of the triangle formed by the lines joining the vertex of the parabola x2 = 20y to the end of the latus rectum? Correct Answer 50 square units

Concept:

Equation of parabola along Y-axis: (x – h)2 = ±4a (y - k),

Here, point (h, k) is vertex of parabola , 4a = length of latus rectum and focus (0, ±a)

Calculation:

Given parabola: x2 = 20y

x2 = 4ay ⇒ a = 5 and vertex = (0, 0)

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∴ Focus = (0, 5)

x2 = 20(5) = 100                

⇒ x = ± 10

AB = 10 + 10 = 20

OM = 5

∴ Area of triangle OAB = ½ × base × height

= 1/2 × (20) × (5)

= 50 sq units

Hence, option (4) is correct.

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