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The straight lines given by the equation 2x^2=2y^2-3xy are:

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The straight lines given by the equation 2x^2=2y^2-3xy are:

by fskilnik@GMATH » Thu Mar 21, 2019 12:08 pm

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GMATH practice exercise (Quant Class 20)

The straight lines given by the equation 2(x^2)=2(y^2)-3xy are:

(A) parallel
(B) intersecting and they form a 30-degrees angle
(C) intersecting and they form a 45-degrees angle
(D) intersecting and they form a 60-degrees angle
(E) intersecting and they form a 90-degrees angle

Answer: [spoiler]______(E)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by fskilnik@GMATH » Thu Mar 21, 2019 1:33 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 20)

The straight lines given by the equation 2(x^2)=2(y^2)-3xy are:

(A) parallel
(B) intersecting and they form a 30-degrees angle
(C) intersecting and they form a 45-degrees angle
(D) intersecting and they form a 60-degrees angle
(E) intersecting and they form a 90-degrees angle
$$?\,\,:\,\,{\rm{lines}}\,\,{\rm{relative}}\,\,{\rm{position}}$$

$$2{x^2} = 2{y^2} - 3xy\,\,\,\, \Leftrightarrow \,\,\,\,2{x^2} - xy = 2{y^2} - 4xy\,\,\,\, \Leftrightarrow $$
$$ \Leftrightarrow \,\,\,\,x\left( {2x - y} \right) = - 2y\left( { - y + 2x} \right)\,\,\,\, \Leftrightarrow \,\,\,\,\left( {2x - y} \right)\left( {x + 2y} \right) = 0$$

$$\left( {2x - y} \right)\left( {x + 2y} \right) = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{
\,2x - y = 0 \hfill \cr
\,\,{\rm{or}} \hfill \cr
\,x + 2y = 0 \hfill \cr} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{
\,y = 2x\,\,\,\,\left( {{\rm{slope}} = 2} \right) \hfill \cr
\,\,{\rm{or}} \hfill \cr
\,y = - {x \over 2}\,\,\,\,\left( {{\rm{slope}} = - {1 \over 2}} \right) \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{E}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
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