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Question

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

A
an ellipse
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B
a parabola
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C
a hyperbola
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D
a pair of straight lines
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Solution

The correct option is B 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
The fixed point (1,0) does not lie on the fixed line 4x3y+1=0
Thus, the given equation represents a parabola.

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