# Write an equation for the circle

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?

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dav2008
Gold Member
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.

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^ thanks

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

That answer looks right to me...What is the answer that is given?
the answer in the book was x^2+y^2=49

dav2008
Gold Member
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?

Are you sure you're checking the answer for the right problem?
ya, the book is old maby that answer is wrong.

Can you see what to do from there?
root 25 is 5 soo..

5root2?

dav2008
Gold Member
Aya said:
root 25 is 5 soo..

5root2?
Yep, that's correct.

k thanks for you help