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Grade 12Analytical Geometry

The length of the chord of the parabola y2=x which is bisected at the point (2,1) is?

a)51/2 b)4*31/2 c)3*31/2 d)2*51/2

Profile image of santosh p
14 Years agoGrade 12
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1 Answer

Profile image of Jit Mitra
14 Years ago

T = S1

y-0.5(x+2) = 1^2 - 2 = -1

 

2y - x - 2 = -2

or, x = 2y

 

Put in the equation,

 

y^2 = 2y

or, y = 0 , 2

x = 0, 4

Points where the line cuts the parabola = (0,0), (4,2)

 

Length = sqrt(4^2 + 2^2) = sqrt(16+4) = sqrt(20) = 2*sqrt(5)

 

Option (d)

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