# Write an equation for the circle

1. May 7, 2006

### Aya

Hi, I need help with these questions

Given the endpoints of a diameter, write an equation for the circle.
a) (-3,5) and (1,3)

I tryed this

m= (x1+x2)/2, (y1+y2)/2
= (-3+1)/2 , (5+3)/2
= -2/2, 8/2
= (-1,4)

( x-h)^2 + (y-k)^2=r^2
(x+1)^2 + (y-4)^2=r^2
(1+1)^2 + (3-4)^2=r^2
(2)^2 + (-1)^2=r^2
5=r^2

so, (x+1)^2 + (y-4)^2 = 5

but, this answer in the back of the book is different so can someone tell me what to do?

and

1. how do you simplify root 50
2. is rise y and run x?

***
when a stone is dropped in a lake, circular waves or ripples are created. The enrey point of the stone marks the center of the circles. Suppose the radious increases at the reate of 20cm/s. write anequation for the outermost circle 2.5s after the stone hits the water.

20*2.5=50cm
X^2 + Y^2=50^2
X^2 + Y^2=2500

is that right?

Last edited: May 7, 2006
2. May 7, 2006

### dav2008

That answer looks right to me...What is the answer that is given?

1) To simplify the square root of 50, can you think of a way to write 50 as the product of two numbers, one of which is a perfect square?

2) Yes. You have to be careful though because it really depends on how you set up your axis. There's nothing stopping you from writing a line in the form of x=my+a, in which case the "rise over run" is a bit misleading if you set up your axis as y vertically and x horizontally.

Last edited: May 7, 2006
3. May 7, 2006

### Aya

^ thanks

I thought the two numbers were 25 and ...but how do you rght that? 2root25
simplify es to 2root5, but thats wrong right?

the answer in the book was x^2+y^2=49

4. May 7, 2006

### dav2008

Are you sure you're checking the answer for the right problem?

You are right that you can write 50 as 25*2

$$\sqrt{50}$$
$$\sqrt{25\cdot 2}$$

Can you see what to do from there?

5. May 7, 2006

### Aya

ya, the book is old maby that answer is wrong.

root 25 is 5 soo..

5root2?

6. May 7, 2006

### dav2008

Yep, that's correct.

7. May 7, 2006

### Aya

k thanks for you help

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