The circle with equation (x-3)^2+(y+4)^2=9 is plotted in the xy-plane. Which of the following ordered pairs (x,y) represents a point on the circle?




Comments (4)

Every question has the mega maven short cut that takes less than 2 minutes ( which is the average time allotment for each question)this one could have been the pattern of the 30 60 90 triangle x= hyp or 3, x/2 = shortside and x/2*square root of 3 is the long side — seeing the 9 they would square root it knowing it was 3 radius and then seeing that it fit with d on the 30 60 90
length pattern. Quick analysis would have told them if they knew the ctr was(3,-4) using the (h,k) center formula, then C was the correct quadrant but wrong placement, A was wrong quadrant as was B — D has that 30 60 90 pattern blaring right at you and answer by default.

But if you are like me and not ivy league material then you would spend about 30 minutes multiplying out (x-3)^2 +(y-4)^2= 9 to get x^2-6x+y^2+8y= -16 –plugging in each answer to learn that d was indeed it but you would know that everyone who was IVY league bound would have been down the page about 5 questions by now.

plug and play

a 9+16 =9 no
b (-6-3*2^.5/2)^2+ (8+3*2^.5/2)^2 =9 no
c 3^2+3^2=9 no
d (3/2 -3^2) = 3/2 ^2 = 9/4 for x

9(3*3^.5)/2)-4 +4 =((3*(3^.5))/2)^2= 9*3/4= 27/4 for y
y +x =9
27/4+9/4 = 36/4 =9 answer d

It seems to me that you can do this much more quickly and efficiently simply by using the points and, more specifically, parts of the points. In other words, you don’t need to calculate using both x and y from each Answer Choice. When I consider y = 4 in Answer A, the squared y-value is 64, which is way high all by itself, eliminating A *and* B, because the y-value for B is 4 plus something. C doesn’t work because the x-value alone = 9 and I’ll be adding to it (because the y-value will be squared and, therefore, positive). Only D is left and, in truth, I don’t even need to check it (though most people will feel compelled to).
Another way to think about this is to consider how a test-writer is going to write these Answer Choices. Is there any way that A or C will work? No, they’re too simple: the test-writers want to force you to do more work than that. So choose the easier of B or D to evaluate, which is clearly D: the +4 and -4 cancel out, making it pretty attractive to calculate. And the 9/4 + 27/4 = 36/4 = 9 is pretty quick work, so you’re done without calculating any of the other 3 Answer Choices.
Ivy League has nothing to do with using the test against itself.

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