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Coordinate Geometry_1

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by jayanti » Fri Aug 12, 2011 6:10 am
In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

A. 3Ï€
B. 3√2π
C. 3√3π
D. 9Ï€
E. 18Ï€

I face a lot of issues on Coordinate Geometry. Can somebody pls explain how to go on topic.

Thanks in anticipation.
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by gmatboost » Fri Aug 12, 2011 8:07 am
Find the distance from the center to the point on the circle using the distance formula.
This is the radius.
Then, use the formula
Area = pi * r^2
to find the area.

Give it a shot and post your thoughts.
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by jayanti » Fri Aug 12, 2011 9:01 am
got 18Ï€ as the answer. Thanks:)

Two questions:

>> To calculate the radius of the circle we use the Distance Formula.
>> How to identify the questions (Data Sufficiency) whether it is asking about the Distance or Slope.

Pls help in advising as I really get confused while working on Coordinate geometry.
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by gmatboost » Mon Aug 15, 2011 8:21 am
Hi Jayanti,

I am not sure what your first question is. We use the distance formula to find the distance between any 2 points (x1, y1) and (x2, y2):
D^2= (x1 - x2)^2 + (y1 - y2)^2 OR
D= sqrt[(x1 - x2)^2 + (y1 - y2)^2]

In this case the distance is from the center to the outside of the circle, so it happens to be the radius.

For distance vs. slope it is difficult to generalize but I would just look for either those words exactly, or related keywords (these are just some examples, not guarantees):
Distance: Length, Far, Side
Slope: Change, Increase, Decrease
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