the area of triangle inscribed in the parabola y^2=4x, the ordinates of whose vertices are 1,2 and 4 is
Answers
Given : triangle inscribed in the parabola y^2=4x, the ordinates of whose vertices are 1,2 and 4 .
To find : area of the triangle
Solution:
y²=4x
ordinate is y coordinate
ordinates of vertices are 1,2 and 4 .
y = 1
=> 1² = 4x
=> x = 1/4
Hence vertex (1/4 , 1)
y = 1
=> 1² = 4x
=> x = 1/4
Hence vertex (1/4 , 1)
y = 2
=> 2² = 4x
=> x = 1
Hence vertex (1 , 2)
y = 4
=> 4² = 4x
=> x = 4
Hence vertex (4 , 4)
Hence vertices of triangle are :
(1/4 , 1) , (1 , 2) and (4 , 4)
Area = (1/2) | (1/4)(2 - 4) + 1(4 - 1) + 4(1-2) |
=(1/2)|-1/2 + 3 - 4|
= (1/2)| -3/2|
= 3/4 sq units
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