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Question
Find the area of the triangle formed by the line joining the vertex of the parabola x2 = 12y to the end points of latus rectum.
Solution
Given equation of the parabola is x2 = 12y.
Comparing this equation with x2 = 4by, we get
4b = 12
∴ b = 3
∴ The co-ordinates of focus are S(0, b), i.e., S(0, 3)
End points of the latus rectum are L(2b, b) and L′(– 2b, b),
i.e., L(6, 3) and L′(– 6, 3)
Also l(LL′) = length of latus rectum
= 4b
= 12
l(OS) = b = 3
Area of the ΔOLL′ = `1/2 xx l("LL"^′) xx l("OS")`
= `1/2 xx 12 xx 3`
∴ Area of the ΔOLL’ = 18 sq. units.
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