Needgmat wrote:In the coordinate plane, a circle has a center (2,-3) and passes through the point (5,0). What is the area of the circle?

A) 3pie

B) 3 under root 2 pie

C) 3 under root 3 pie

D) 9 pie

E) 18 pie

OAE

Hi Experts ,

I have to do coordinate geometry from the starting. Please advise from where should I do?

Thanks,

Kavin

Hi Kavin,

For coordinate geometry, you need to understand the basics of the geometry too. That will help you in visualising the diagram.
1. Understand the XY axes
2. Distance between two points
3. Slope of a line
4. Relation between slope of two lines.

There are some of the things that you should be well versed with.

As for the question, since the circle passes through (5,0) the radius will be the line joining the centre (2,-3) and (5,0)
Length of radius = (3^2+3^2)^(1/2) = 18^(1/2)

Area = π*r^2 = π*18

Correct Option: E

Needgmat wrote:In the coordinate plane, a circle has a center (2,-3) and passes through the point (5,0). What is the area of the circle?

A) 3pie

B) 3 under root 2 pie

C) 3 under root 3 pie

D) 9 pie

E) 18 pie

Because the circle passes through point (5,0) and has center (2,-3), we know that the distance between these points is the radius of the circle.

Since we are given the coordinates for each point, the easiest thing to do is to use the distance formula to determine the circle's radius. The distance formula is:

Distance= √[(x2 - x1)^2 + (y2 - y1)^2]

We are given two ordered pairs, so we can label the following:

x1 = 2
x2 = 5

y1 = -3
y2 = 0

When we plug these values into the distance formula, we have:

Distance= √[(5 - 2)^2 + (0 - (-3))^2]

Distance= √[(3)^2 + (3)^2]

Distance= √[9 + 9]

Distance = √[18] = √9 x √2 = 3 x √2

Thus, we know that the radius = 3 x √2.

Finally, we can use the radius to determine the area of the circle.

area = πr^2

area = π(3 x √2)^2 = 18π

Answer: E