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Question

The equation
25[x2+y22x+1]=(4x3y+1)2 represents

A
Parabola
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B
Circle
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C
Pair of straight line
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D
None of these
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Solution

The correct option is A Parabola
The given equation is
25[x2+y22x+1]=(4x3y+1)2(1)
The right hand side of this equation can be written in the form of perpendicular distance
(4x3y+1)2=25⎜ ⎜4x3y+1(42+32)⎟ ⎟2
then equation (1) can be re-written as
25[(x1)2+(y0)2]=25⎜ ⎜4x3y+1(42+32)⎟ ⎟2
(x1)2+(y0)2=|4x3y+1|42+32
here e=1
Thus the given equation represents a parabola. It may noted that (1,0) is the focus and 4x3y+1=0 is the directrix of the parabola.

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