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# Describing the shape of the curve watch

1. I have an equation of the the following function:
d(x^2+y^2) + 2(ax-by)+c = 0 where a,b, c and d are reals.
Could someone please explain how I could explain the shape of the curve when d=0 and d is not equal to 0.
For d=0 we get a line.
But for d not equal to 0 do we get a circle? I guess I could complete the square for x and y and so obtain an equation for a circle, is that correct?
Thank you!
2. (Original post by spacewalker)
I have an equation of the the following function:
d(x^2+y^2) + 2(ax-by)+c = 0 where a,b, c and d are reals.
Could someone please explain how I could explain the shape of the curve when d=0 and d is not equal to 0.
For d=0 we get a line.
But for d not equal to 0 do we get a circle? I guess I could complete the square for x and y and so obtain an equation for a circle, is that correct?
Thank you!
Yes, correct.
3. (Original post by spacewalker)
But for d not equal to 0 do we get a circle? I guess I could complete the square for x and y and so obtain an equation for a circle, is that correct?
I would add a caveat to what NotNotBatman has said.

For , if you rearrange into the form , then what's on the righthand side needs to be positive for a circle. If it's zero, your equation defines a point (circle radius zero), and if it's negative, there's no real solution.
4. (Original post by ghostwalker)
I would add a caveat to what NotNotBatman has said.

For , if you rearrange into the form , then what's on the righthand side needs to be positive for a circle. If it's zero, your equation defines a point (circle radius zero), and if it's negative, there's no real solution.
Nice, I missed that.

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