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Equation of a circle.......

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by pzazz12 » Tue Oct 19, 2010 1:57 am
What is the equation of a circle of radius 6 units centered at (3, 2)?

A. x2 + y2 + 6x - 4y = 23
B. x2 + y2 - 6x + 4y = 23
C. x2 + y2 + 6x + 4y = 23
D. x2 + y2 - 6x - 4y = - 23
E. x2 + y2 - 6x - 4y = 23
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by shovan85 » Tue Oct 19, 2010 2:30 am
The general formula of a circle with origin at point (a,b) and radius r is

(x-a)^2 + (y-b)^2 = r^2.

Put the values and get the answer.

IMO E
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by kvcpk » Tue Oct 19, 2010 3:00 am
pzazz12 wrote:What is the equation of a circle of radius 6 units centered at (3, 2)?

A. x2 + y2 + 6x - 4y = 23
B. x2 + y2 - 6x + 4y = 23
C. x2 + y2 + 6x + 4y = 23
D. x2 + y2 - 6x - 4y = - 23
E. x2 + y2 - 6x - 4y = 23
Eqtn of a circle is out of scope for GMAT. Make sure you study from right sources.
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by Ramneet Singh » Tue Oct 19, 2010 3:21 am
pzazz12 wrote:What is the equation of a circle of radius 6 units centered at (3, 2)?

A. x2 + y2 + 6x - 4y = 23
B. x2 + y2 - 6x + 4y = 23
C. x2 + y2 + 6x + 4y = 23
D. x2 + y2 - 6x - 4y = - 23
E. x2 + y2 - 6x - 4y = 23
The equations can also be
x2 + y2 + 2gx + 2fy +c=0
radius=sqrt(g2 + f2 -c)
g=-h
f=-k
The centre of circle is (h,k)
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by fskilnik@GMATH » Tue Oct 19, 2010 4:17 am
kvcpk wrote:Eqtn of a circle is out of scope for GMAT.
Hi kvcpk,

IMHO I would not count on that... from my experience, the equation presented by Shovan is AT LEAST extremely useful in some GMAT questions, although I agree that you could use the "Geometry" of the Pythagorean triangle that gives "birth" to it in most cases.

The fact that it is easily deduced and understood, and may save some time in some problems, makes me recommend my students to know it and to use it whenever needed. (But it is only my point-of-view, of course.)
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by GMATGuruNY » Tue Oct 19, 2010 5:33 am
pzazz12 wrote:What is the equation of a circle of radius 6 units centered at (3, 2)?

A. x2 + y2 + 6x - 4y = 23
B. x2 + y2 - 6x + 4y = 23
C. x2 + y2 + 6x + 4y = 23
D. x2 + y2 - 6x - 4y = - 23
E. x2 + y2 - 6x - 4y = 23
The GMAT does not test the equation of a circle (nor does it test the equation of a parabola, a hyperbola, an ellipse, a sphere, or a pyramid).

That being said, there is a good take-away here. Since we know that r=6, just plug into all the answer choices the coordinates of a point 6 units from (3,2), such as (-3,2):

Answer choice E:
(-3)^2 + 2^2 - 6*(-3) - 4*2 = 9+4+18-8 = 23.

The correct answer is E.
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by fskilnik@GMATH » Tue Oct 19, 2010 6:14 am
GMATGuruNY wrote:The GMAT does not test the equation of a circle... there is a good take-away here....
As I said, pzazz12, you must choose what you prefer... avoid a simple (and I repeat easily deductible and understandable) formula or use something like what the GMATGuruNY suggests.

I guess it´s not a matter of what is better, I believe it´s a matter of what is better for each person (taking into account the stress restrictions/conditions of the GMAT, for sure).
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by fskilnik@GMATH » Tue Oct 19, 2010 7:47 am
fskilnik wrote:... or use something like what the GMATGuruNY suggests.
I am not an English-native speaker and I must say there was no pun intended here. Sorry for any misunderstanding.

GMATGuruNY: the solution you presented at the link below was really impressive, by the way. Congrats!

Link: https://www.beatthegmat.com/positive-int ... 68499.html
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by GMATGuruNY » Tue Oct 19, 2010 2:32 pm
fskilnik wrote:
fskilnik wrote:... or use something like what the GMATGuruNY suggests.
I am not an English-native speaker and I must say there was no pun intended here. Sorry for any misunderstanding.

GMATGuruNY: the solution you presented at the link below was really impressive, by the way. Congrats!

Link: https://www.beatthegmat.com/positive-int ... 68499.html
Thanks, fsk!
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by frank1 » Tue Oct 19, 2010 7:44 pm
GMATGuruNY wrote:
The GMAT does not test the equation of a circle (nor does it test the equation of a parabola, a hyperbola, an ellipse, a sphere, or a pyramid).
.
well guru,Can we take it as rule?
I have also not seen such question till now in any prep.
But
the quantative review OG has a page dedicated to parabola and its equation.
So only because of that sometime i am doubtful.

thanks.
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by GMATGuruNY » Wed Oct 20, 2010 4:20 am
frank1 wrote:
GMATGuruNY wrote:
The GMAT does not test the equation of a circle (nor does it test the equation of a parabola, a hyperbola, an ellipse, a sphere, or a pyramid).
.
well guru,Can we take it as rule?
I have also not seen such question till now in any prep.
But
the quantative review OG has a page dedicated to parabola and its equation.
So only because of that sometime i am doubtful.

thanks.
The GMAT does not test the equation of a circle, of a hyperbola, of an ellipse, of a sphere, of a cone, or of a pyramid. If the equation of any of these shapes is needed in order to solve a GMAT problem (unlikely), the equation will be given.

Since a parabola is the basic quadratic equation y = a^2+bx+c, it might be discussed, but only in a very rudimentary way. It might be helpful to know the following:

If a>0, the parabola opens upward and looks like this: U. Its minimum value is -b/2a. Its y intercept is c.

So given y = 2x^2+4x+5:
It opens upward and looks like a U.
Its minimum value is -4/(2*2) = -1.
It intersects the y axis at y=5.

If a<0, the parabola opens downward and looks like this: ∩. Its maximum value is -b/2a. Its y intercept is c.

So given y = -2x^2+4x+5:
It opens downward and looks like a ∩.
Its maximum value is -4/(2*-2) = 1.
It intersects the y axis at y=5.

A parabola is symmetrical about the vertical line that would split it down the middle. This line (called the axis of symmetry) passes through the minimum or maximum value of the parabola. Thus, the equation of the axis of symmetry is x = -b/2a.

Helpful info, but I'd be surprised if you need it when you take the GMAT.
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