# Example 11

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 11 Find the area of the parabola 𝑦2=4𝑎𝑥 bounded by its latus rectum For Parabola 𝑦2=4 𝑎𝑥 Latus rectum is line 𝑥=𝑎 Area required = Area OLSL’ =2 × Area OSL = 2 × 0𝑎𝑦 𝑑𝑥 𝑦 → Parabola equation 𝑦2=4 𝑎𝑥 𝑦=± 4 𝑎𝑥 Since OSL is in 1st quadrant 𝑦= 4 𝑎𝑥 Area required = 2 × 0𝑎𝑦 𝑑𝑥 = 2 0𝑎 4 𝑎𝑥 𝑑𝑥 = 2 0𝑎 4 𝑎 𝑥 𝑑𝑥 = 2 4 𝑎 0𝑎 𝑥 𝑑𝑥 = 4 𝑎 0𝑎 𝑥 𝑑𝑥 = 4 𝑎 𝑥 32 320𝑎 = 4 𝑎 × 23 𝑥 320𝑎 = 83 𝑎 𝑎 32−0 = 83 𝑎 𝑎 32 = 83 𝑎 12 𝑎 32 = 83 𝑎 12 + 32 = 83 𝑎 42 = 𝟖𝟑 𝒂𝟐

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Davneet Singh

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