A circle is drawn in the xy-coordinate plane. If there are n differen

Question

A circle is drawn in the xy-coordinate plane. If there are n different points (x, y) on the circle such that xy = 0, then the possible values of n are:

a) 0, 1, or 2
 
b) 0, 2, or 4
 
c) 0 or 4
 
d) 0, 2, 3, or 4
 
e) 0, 1, 2, 3, or 4

Kurtosis · Accepted Answer

Given: xy = 0 --> xy is a line on the x axis or y axis
We have to find the number of points of intersection of xy with the circle.

As seen in the attached figure, answer is E.

Bunuel · Answer

This is the case when the condition is not satisfied, so when the answer is that there are 0 points (x, y) on the circle such that xy = 0.

kannu44 · Answer

When Circle is not touching any of the X axis or Y axis, how the condition xy=0 is satisfied ?
could you please explain.
thanks for your help

vrindachopra · Answer

For n = 4, how is the condition x*y = 0 satisfied ?? In the figure attached, neither x nor y is 0 for n = 4 ! So how is the case satisfied ??

Arsh4MBA · Answer

Bunuel  could u pls explain what is this question asking for? kind of ambiguous for me

adkikani · Answer

Bunuel   chetan2u   niks18

Is not this kind of an universal truth? A circle is a 2D figure. 
What do I infer from this sentence?

How do I make sure: (x,y) refer to circumference and not area?
Can I infer we are talking about intercepts from (x,y) = 0?

chetan2u · Answer

Is not this kind of an universal truth? A circle is a 2D figure. 
What do I infer from this sentence?
 Yes it is a 2D figure. but it could be xz or yz although we normally talk of xy coordinates... so its OK as we are dealing with x,y thereafter

How do I make sure: (x,y) refer to circumference and not area?
Can I infer we are talking about intercepts from (x,y) = 0?
 Since it is given ON the circle, it is talking of (x,y) lying on the circumference..
Had it been IN the circle, we would have talked about area

adkikani · Answer

chetan2u

What is z in in your reply?

Ideally a single point on / inside the circle will still be represented only by an order pair (x,y)

This not a sphere Q, representing (x,y,z) . Why is at all is first sentence required to be given?

chetan2u · Answer

what if I draw it on ground or on wall... both are different planes..

But as I told you , you dont have to worry about it. But mentioning a circle in xy-coordinate is perfectly fine

Princ · Answer

xy plane can be written as (x,y,0).
z = 0 for xy plane. similarly xz plane would be (x,0,z) ,y will be zero in xz plane. It is possible to have equation of circle as  x^2+z^2=16  in xz plane

Sent from my XT1068 using  GMAT Club Forum mobile app

GMATBusters · Answer

But as the question explicitly states points (x,y) lies on circle, hence it is in xy plane.

There is no point in contemplating about different other planes possible.

Posted from my mobile device

JIAA · Answer

Math experts can you please help explain this? as in visually???
Since xy=0, i do understand that either x or y or both can be 0. But how do i assume different points on the xy coordinate?

soapbolt · Answer

VQ

Question ask us to find the possible value of n where xy=0

It means we need to find the case when points on the circle can have value as xy = 0 (i.e. Minimum to maximum values)

as explained by Vyshak visually , n can take value from 0 to 4

Hope it helps

Shrey9 · Answer

Lets say if this question had an option of 7-8 integers starting from 0-7 (same as E)..
That would have been our answer in that case ?

Main point to note is that : It must contain a 0 and all other maximum possible points, right. ?

njnikhiljindal567 · Answer

In the figure, the largest circle is the case with 4 points. 
When the circle crosses any of the points on the axis either x=0 or y=0 and hence xy=0

Fdambro294 · Answer

Effectively, the Question is Asking us:

What are the Different ways in which we can draw a Circle in the Coordinate Plane in which the Circle either crosses or does NOT cross the Y-Axis or X-Axis?

(1st) We can draw the Circle immediately inside 1 Quadrant, in which there are NO X- or Y-Intercepts

n = 0 ---- there will be NO Coordinates for which X * Y = 0

(2nd) We can draw a Circle such that it is TANGENT to 1 of the Axis and does NOT Cross either Axis anywhere else.

This would give us 1 Coordinate that would have either X or Y = 0 ----- and X * Y = 0

n = 1

(3rd) We can draw a Circle such that it Intersects just the (+)Positive Portion of the Y-Axis TWICE

As an Example, the Y-Axis could completely BISECT the Circle in Half.

There would be 2 Points in which X = 0 ---- 2 Y-Intercepts ---- and the Coordinates Multiplied would be X * Y = 0

n can be = 2

(4th) ***this is the one I struggled with at 1st

Can we draw a Circle in the Plane such that it has 3 Intercepts and NO MORE?

EX: We Draw the Circle so that the TOP of the Circle is Tangent to the (+)Positive X-Axis

Then, we allow the Left Side of the Circle to Intersect the (-)Negative Y-Axis TWICE, as it Circles around

In this case, we would have 3 Coordinates in which either X = 0 or Y = 0 ----

n can = 3

Finally, we know n can = 4 if we have a Circle drawn with the Origin as the Center.

-E-

n can = 0 , 1 , 2 , 3 , or 4

Gau0809 · Answer

I got confused because of the language. It sounds as if the question is asking us, about number of points n(x,y) a circle can cross the axes such that xy=0.
I mean it is not explicitly clear whether the question wants to ask how many different such circles can be formed.

Can someone help me to understand where did I go wrong?
 Bunuel

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A circle is drawn in the xy-coordinate plane. If there are n differen

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A circle is drawn in the xy-coordinate plane. If there are n differen

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