Misc 6 - Find area of triangle formed by the lines joining - Parabola - Triangle in parabola problem

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Misc 6 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. The given equation of parabola is x2 = 12y The above equation is of the form x2 = 4ay Comparing (1) & (2) 12y = 4ay ﷐12𝑦﷮4𝑦﷯ = a 3 = a a = 3 Let AB be the latus rectum And Δ AOB be the required triangle Now, a = 3 Hence, OP = 3 Width of latus rectum = 4a = 4 × 3=12 AB = 12 Area of triangle AOB = ﷐1﷮2﷯ × Base × Altitude = ﷐1﷮2﷯ × AB × OP = ﷐1﷮2﷯ × 12 × 3 = 18 square units

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