Do these lines intersect ?

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tennisstar: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Mar 28, 2010 12:18 pm; Thanked: 1 times

by tennisstar » Fri Nov 11, 2011 1:29 pm

Do lines y = ax^2 + b and y =cx^2 + d cross?

A:a = -c
B:b>d

how to solve this kind of questions? what is m for both lines as we have x^2 in line equation.?what is condition to check that line are crossing each other or not?

source: gmatclub test

Thanks much,

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Source: Beat The GMAT — Data Sufficiency | Fri Nov 11, 2011 1:29 pm

user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Fri Nov 11, 2011 1:57 pm

tennisstar wrote:Do lines y = ax^2 + b and y =cx^2 + d cross?

A:a = -c
B:b>d

how to solve this kind of questions? what is m for both lines as we have x^2 in line equation.?what is condition to check that line are crossing each other or not?

source: gmatclub test

Thanks much,

IMO E

1) to find the common points between two lines, we need to solve both equations and find valid values for x & y
consider a = -c
=> y = -cx^2+b & y = cx^2 +d
solving for x
-cx^2+b = cx^2 +d
2cx^2 = d-b
x = root((d-b)/2c)
if c +ve and d-b >= 0 then we get valid x
if c +ve and d-b <= 0 then we get imaginary x
if c -ve ....
if c -ve ....
hence not sufficient.
2) b > d
solve again both for x
ax^2+b = cx^2 +d
x^2(c-a) = b-d
x = root(b-d / c-a)
we know b-d>0 but not about c-a. hence insufficient.

if both used
we know
x = root((d-b)/2c)
though d-b>0 we dont know the sign of c. hence still insufficient.

user123321

Just started my preparation

Want to do it right the first time.

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tennisstar: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Mar 28, 2010 12:18 pm; Thanked: 1 times

by tennisstar » Sat Nov 12, 2011 1:20 am

There is a mistake:

=> y = -cx^2+b & y = cx^2 +d

solving for x

-cx^2+b = cx^2 +d

2cx^2 = d-b >>>>>>>>>>>>>>>>>>>>>> 2cx^2 = b - d and NOT (d-b)

So, x = root((b-d)/2c)

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sat Nov 12, 2011 1:25 am

How can a quadratic equation be a line? Are you sure of the question?

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tennisstar: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Mar 28, 2010 12:18 pm; Thanked: 1 times

by tennisstar » Sat Nov 12, 2011 2:01 am

I am afraid but this is the actual question taken from gmat club test 24. The OA is E

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user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Sat Nov 12, 2011 4:52 am

tennisstar wrote:There is a mistake:

=> y = -cx^2+b & y = cx^2 +d

solving for x

-cx^2+b = cx^2 +d

2cx^2 = d-b >>>>>>>>>>>>>>>>>>>>>> 2cx^2 = b - d and NOT (d-b)

So, x = root((b-d)/2c)

it is a small typo. But still the concept & answer remains the same.
yet we dont know whether b-d>0 and c>0 (or) b-d<0 and c<0 to get valid x. hence insufficient.

user123321

Just started my preparation

Want to do it right the first time.

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user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Sat Nov 12, 2011 4:55 am

shankar.ashwin wrote:How can a quadratic equation be a line? Are you sure of the question?

Any equation can form a line. A special case is linear equation with one or two variable, which forms a straight line.

user123321

Just started my preparation

Want to do it right the first time.

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tennisstar: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Mar 28, 2010 12:18 pm; Thanked: 1 times

by tennisstar » Sat Nov 12, 2011 5:34 am

user123321 wrote:
tennisstar wrote:There is a mistake:

=> y = -cx^2+b & y = cx^2 +d

solving for x

-cx^2+b = cx^2 +d

2cx^2 = d-b >>>>>>>>>>>>>>>>>>>>>> 2cx^2 = b - d and NOT (d-b)

So, x = root((b-d)/2c)
it is a small typo. But still the concept & answer remains the same.
yet we dont know whether b-d>0 and c>0 (or) b-d<0 and c<0 to get valid x. hence insufficient.

user123321

Yeah, the concept n ans remains the same. Thx a lot

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mankey: Legendary Member; Posts: 627; Joined: Thu Jun 23, 2011 9:12 amFollowed by: 1 member; Thanked: 4 times

by mankey » Sun Nov 13, 2011 10:50 am

Is it right to call a quadratic equation a line? It will be a parabola, which is part of conic sections.

All equations in x can be called "curves" but not sure if they can be called lines!!

Some expert please clarify.

Thanks.

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