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# A curve is represented by the equation x^2y^3 = k^3

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Joined: 04 Jan 2015
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A curve is represented by the equation x^2y^3 = k^3  [#permalink]

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27 Aug 2018, 02:35
00:00

Difficulty:

65% (hard)

Question Stats:

39% (01:09) correct 61% (01:30) wrong based on 93 sessions

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A curve is represented by the equation $$x^2y^3 = k^3$$, where k < 0. At how many points does the line, y = -a, where a is an integer, intersects this curve?

A. 0
B. 1
C. 2
D. 4
E. Cannot be determined

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Re: A curve is represented by the equation x^2y^3 = k^3  [#permalink]

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27 Aug 2018, 03:22
Guess: Since the value of y is always negative, if a is +ve then it cuts the graph at 2 points and if a is -ve then 0 points. Hence cannot be determined.
E??

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A curve is represented by the equation x^2y^3 = k^3  [#permalink]

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27 Aug 2018, 04:54
1
can someone sketch solution ? its like chinese to me reading only text without visualization
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Re: A curve is represented by the equation x^2y^3 = k^3  [#permalink]

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27 Aug 2018, 05:10
1
dave13 wrote:
can someone sketch solution ? its like chinese to me reading only text without visualization

This graph looks familiar. Oh wait!!!

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File comment: My view of the graph. Open to critique.

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Re: A curve is represented by the equation x^2y^3 = k^3  [#permalink]

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27 Aug 2018, 05:18
2
1
EgmatQuantExpert wrote:
A curve is represented by the equation $$x^2y^3 = k^3$$, where k < 0. At how many points does the line, y = -a, where a is an integer, intersects this curve?

A. 0
B. 1
C. 2
D. 4
E. Cannot be determined

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IMHO answer is E
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1535375933597.jpg [ 56.24 KiB | Viewed 911 times ]

Thank you = Kudos
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A curve is represented by the equation x^2y^3 = k^3  [#permalink]

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27 Aug 2018, 05:19
1
EgmatQuantExpert wrote:
A curve is represented by the equation $$x^2y^3 = k^3$$, where k < 0. At how many points does the line, y = -a, where a is an integer, intersects this curve?

A. 0
B. 1
C. 2
D. 4
E. Cannot be determined

The correct answer is (E):

$$\left\{ \begin{gathered} \,{x^2}{y^3} = {k^3}\,\,\,\left( {k < 0} \right) \hfill \\ y = - a\,\,\,\left( {a\,\,\operatorname{int} } \right) \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,{x^2}{\left( { - a} \right)^3} = {k^3}\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,{x^2} = - {\left( {\frac{k}{a}} \right)^3}\,\,\,\,\,,\,\,\,\,a \ne 0$$

Take (for instance) :

(a,k) = (1,-1) , then we have 2 points (x,y) = (x, -a) of intersection: (-1, -1) and (1, -1)
(a,k) = (-1,-1) , then we have 0 points (x,y) = (x,-a) of intersection, because x^2 = -1 has no solutions (in the real numbers)

The above follows the notations and rationale taught in the GMATH method.
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Re: A curve is represented by the equation x^2y^3 = k^3  [#permalink]

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27 Aug 2018, 05:29
1
x^2 is acting as magnitude and y^3 goes from +ve infinite to -ve infinite so it will at least cut y=-a one. so answer is B.
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Joined: 28 Jun 2018
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Re: A curve is represented by the equation x^2y^3 = k^3  [#permalink]

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12 Sep 2018, 08:57
Bunuel can you please explain this?
Re: A curve is represented by the equation x^2y^3 = k^3 &nbs [#permalink] 12 Sep 2018, 08:57
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# A curve is represented by the equation x^2y^3 = k^3

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