Decide if the equation defines an ellipse, a hyperbola, a parabola, or no conic section at all.displaystyle{left({a}right)}{4}{x}{2}-{9}{y}{2}={12}{left({b}right)}-{4}{x}+{9}{y}{2}={0}displaystyle{left({c}right)}{4}{y}{2}+{9}{x}{2}={12}{left({d}right)}{4}{x}{3}+{9}{y}{3}={12}

midtlinjeg 2020-11-24 Answered

Decide if the equation defines an ellipse, a hyperbola, a parabola, or no conic section at all.
(a)4x29y2=12(b)4x+9y2=0
(c)4y2+9x2=12(d)4x3+9y3=12

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Expert Answer

diskusje5
Answered 2020-11-25 Author has 82 answers
Standard equation of ellipse:
x2a2+y2b2=1
Standard equation of a parabola:
y2=4ax
Standard equation of a Hyperbola:
x2a2y2b2=1
a)
4x29y2=12
Divide by coefficient of square terms : 4
x294y2=3
Divide by coefficient of square terms : 9
19x214y2=13
Divide by 13
x23y243=1
So, this is the form of hyperbola x2a2y2b2=1
Thus, the equation 4x29y2=12 defines a hyperbola.
b)
4x+9y2=0
9y2=4x
y2=4x9
So, this is the form of parabola y2=4ax
Thus, the equation 4x+9y2=0 defines a parabola.
c)
4y2+9x2=12
Divide by coefficient of square terms : 9
x2+49y2=43
Divide by coefficient of square terms : 4
14x2+19y2=13
Divide by 13
x243+y23=1
This is the form of ellipse x2a2+y2b2=1
Thus, the equation 4y2+9x2=12 defines an ellipse.
d)
4x3+9y3=12
The above equation is not an ellipse, parabola and a hyperbola.
Hence, the equation 4x3+9y3=12 is not a conic section.
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