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
12 4 = a
3 = a
a = 3
Let AB be the latus rectum
And 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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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