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Does equation (5x-5)^(2)+(5y+10)^(2)=(3x...

Does equation `(5x-5)^(2)+(5y+10)^(2)=(3x+4y+5)^(2)` represents a parabola ?

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Verified by Experts

We have `(5x-5)^(2)+(5y+10)^(2)=(3x+4y+5)^(2)`
`:." "sqrt((x-1)^(2)+(y+2)^(2))=(|3x+4y+5|)/(5)`
L.H.S = distance of variable point P(x,y) from fixed point (1,-2)
R.H.S. = distance of point P(x,y) from the fixed line `3x+4y+5=0`
But point (1,-2) satisfies the line `3x+4y+5=0`.
So, equation does not represent a parabola.
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