Question
Download Solution PDFThe area of the region bounded by the parabola y2 = 4kx, where k > 0 and its latus rectum is 24 square units. What is the value of k ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
The equation of parabola is y2 = 4kx ------(1)
Let O be the vertex, S be the focus, and LL' be the latus rectum of the parabola.
The equation of latus rectum is x = k.
Also, here the parabola is symmetric about x−axis.
Required area, A = 2(area of OSL)
⇒ Required area, A = 2
⇒ A = 2
⇒ A = 2.2√k
⇒ A = 4√k
⇒ A =
⇒ A =
Since the area of the given parabola is 24.
⇒ 24 =
⇒ k = ± 3
As the value of k > 0, k = 3.
∴ The value of k = 3.
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