How would you classify this curve?
9y^2 + 16x^2 – 20y + 15x + 24xy = 0
Is it
a) an ellipse
b) a parabola
c) a hyperbola
d) none of the above
2007-10-06 02:44:14 · 5 answers · asked by Dr D 7 in Science & Mathematics ➔ Mathematics
discriminant:
B^2 - 4AC = (24)^2 - 4(16)(9) = 0
thus this is a parabola or a degenerate parabola... depending on the outcome after rotation...
the angle of rotation is 1/2 arccot(7/24)
after rotation it becomes...
25 x'^2 - 25y' = 0
y' = x'^2
thus the answer is B.
2007-10-06 03:05:54 · answer #1 · answered by Alam Ko Iyan 7 · 2⤊ 0⤋
The answer is "d", none of the above. None of the shapes given in the other answers has an "xy" term.
Correction: I was incorrect. The answer is really B, as others have already said. A parabola may have an XY term. My mistake.
2007-10-06 03:04:21 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Why don't you know the answer yourself Dr?
The curve, if indeed it is a curve has one point that is the origin of both the x and y axies. At Zero. The value of either x or y will be a negative value if there is in fact any solution to the equation. I can't be bothered to look at this any longer.
2007-10-06 03:06:30 · answer #3 · answered by Will in Spain 2 · 0⤊ 3⤋
none of the above. the eqns of ellipse, parabola and hyperbola do not have xy term...
2007-10-06 02:54:04 · answer #4 · answered by tootoot 3 · 0⤊ 0⤋
b) as you can write is as (4x+3y)^2 +5(3x-4y)=0
2007-10-06 02:52:36 · answer #5 · answered by santmann2002 7 · 1⤊ 0⤋