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22 Sep 2009, 00:28
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hi
i have few hard DS problems in co-geo.plz help me in order to solve these q's.
Regards
Raghav
i have few hard DS problems in co-geo.plz help me in order to solve these q's.
Regards
Raghav
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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24 Sep 2009, 23:35
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ANSWER TO Q3:
Firstly, note that the equation y=(x+a)(x+b) is a parabola. It will intersect the x-axis at two points.
Statement 1
We can't do anything with this equation. Combined with the equation given in the stem of the question, thee are still 4 variables and only 2 equations.
Statement 2
This means x =0, y=-6. Plugging this into the original equation:
-6=(0+a)(0+b)
-6=ab
Possible values of a and b can be: (6,-1), (-1,6), (3,-2), (2,-3). There is insufficient information to determine which exactly set of values of a and b we should choose however.
Statement 1 and 2 combined
A+b=-1
-6=ab
A unique pairing of a,b can be determined : -3, 2
Note that we are just asked to find the points at which the graph intersects the x-axis. We do not need to know exactly which value is a or b. A can be -3 or 2 and vice versa for b.
So, (x-3)(x+2)=y
To find the point of intersection, let y=0 and solve accordingly:
X-3=0, x=3
X+2=o, x=-2
The graph will intersect at (3,0), (-2,0)
Both statements are sufficient.
Firstly, note that the equation y=(x+a)(x+b) is a parabola. It will intersect the x-axis at two points.
Statement 1
We can't do anything with this equation. Combined with the equation given in the stem of the question, thee are still 4 variables and only 2 equations.
Statement 2
This means x =0, y=-6. Plugging this into the original equation:
-6=(0+a)(0+b)
-6=ab
Possible values of a and b can be: (6,-1), (-1,6), (3,-2), (2,-3). There is insufficient information to determine which exactly set of values of a and b we should choose however.
Statement 1 and 2 combined
A+b=-1
-6=ab
A unique pairing of a,b can be determined : -3, 2
Note that we are just asked to find the points at which the graph intersects the x-axis. We do not need to know exactly which value is a or b. A can be -3 or 2 and vice versa for b.
So, (x-3)(x+2)=y
To find the point of intersection, let y=0 and solve accordingly:
X-3=0, x=3
X+2=o, x=-2
The graph will intersect at (3,0), (-2,0)
Both statements are sufficient.
24 Sep 2009, 23:45
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ANSWER TO Q2
It helps if you actually draw this out. The circle will have its origin at 0, and touch on points 1 and -1 on the x axis and 1 and -1 on the y axis
1) Insufficient as the line can either pass through or not pass through the circle. Try drawing it and see. You need the slope to find out if line k will intersect the circle.
2) With this slope, you either go left by one unit and up by 10 from any point on the x axis, and/or go right by one unit and go down by 10 from any point on the x axis. Either way, the line WILL pass through the circle. I'm not sure how to prove this mathematically though. It would help if someone could explain.
As I said, it helps if you draw it out.
It helps if you actually draw this out. The circle will have its origin at 0, and touch on points 1 and -1 on the x axis and 1 and -1 on the y axis
1) Insufficient as the line can either pass through or not pass through the circle. Try drawing it and see. You need the slope to find out if line k will intersect the circle.
2) With this slope, you either go left by one unit and up by 10 from any point on the x axis, and/or go right by one unit and go down by 10 from any point on the x axis. Either way, the line WILL pass through the circle. I'm not sure how to prove this mathematically though. It would help if someone could explain.
As I said, it helps if you draw it out.
