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Question

The common tangent of the two parabolas y2=4x and x2=32y meets the coordinate axes at A,B respectively. The equation of the circumcircle of ΔOAB is

A
x2+y24x2y=0
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B
x2+y2+4x+2y=0
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C
x2+y2+2x+y=0
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D
x2+y22xy=0
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Solution

The correct option is B x2+y2+4x+2y=0
Equation of a tangent to y2=4x in slope form is
y=mx+1m (a=1)
It also touches x2=32y
x2=32(mx+1m) has equal roots.
x232mx32m=0 has equal roots.
D=0(32m)2+4(32m)=0
m3=18
m=12

Equation of common tangent is x+2y+4=0
Here, A=(4,0), B=(0,2)

Equation of circumcircle of ΔOAB is
(x+4)(x0)+(y0)(y+2)=0 (AB is diameter)
x2+y2+4x+2y=0

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