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

Question

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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sumit411 · Accepted Answer

IMHO answer is E 1535375999030.jpg Thank you = Kudos

Addupaddukaddu · Answer

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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dave13 · Answer

can someone sketch solution ?

its like chinese to me reading only text without visualization

Addupaddukaddu · Answer

This graph looks familiar. Oh wait!!!

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fskilnik · Answer

The correct answer is (E):

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

Abhinav kumar · Answer

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.

hibobotamuss · Answer

Bunuel  can you please explain this?

georgecambridge · Answer

can someone clarify it?

ZIX · Answer

Here's an easier approach:

the line  y = -a  would always have x coordinate = 0, since we are just moving on the y axis. So the first line must cross y axis when x = 0.

now  (x^2)(y^3)=k^3 
 y^3 =\frac{k^3}{x^2}

However, when we set x = 0, we would have to divide it by 0 which is not possible. So the answer is "can't be determined".

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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