Urgent!! please help!!!!?

Question

how would you find the center and radius of this equation?? I missed the class, and I don't have the notes yet!! Please help!!

X^2 + y^2 = 16

and could someone please tell me how to MAKE and equation from the points??

Center (0,0) radius =5

Please explain how you get each answer!! I don't just want the answers!! thank you soooooooo much!!!

i didnt miss class cause i was skipping or anything!! I was in a different class!! It was required, i didnt have any choice!!!

Answer 1

The equation of a circle at the origin (0,0) with radius r is:

x² + y² = r²

So in your example (x² + y² = 16), the radius is 4.

And for the second equation, you just go the opposite direction:

x² + y² = 5²
x² + y² = 25

Note: this is derived from the Pythagorean theorem. If you imagine a point (x, y) on the circle, you can draw a right-triangle to that point. The legs will be x and y and the hypotenuse will be the radius of the circle (r). From there it is easy to get the equation x² + y² = r². See the attached picture if it isn't clear.

As long as we are talking about the formula for a circle, let me give you an expanded equation for a circle that isn't at the origin:

(x - x1)² + (y - y1)² = r²

Here x1 and y1 are the coordinates of the center. So if they asked you to give the equation for a circle with a center of (3, 4) and a radius of 5, the answer would be:

(x - 3)² + (y - 4)² = 5²

This is derived the same way as the other formula, but just by offsetting the x and y coordinates.

There you go... a full class lecture in a couple minutes on Yahoo Answers! :-)

Answer 2

You missed the class on circles
the standard equat of a circle with center (0, 0) is
x² + y² =r², where r is the radius
since the equation you have is in that form
x² + y² = 16
x² + y² =(4)²
the radius is 4 and center (0 , 0)

Center (0,0) radius =5
since center is (0 , 0) we just use the standard form

x² + y² =r² so we have x² + y² =(5)²
which gives x² + y² = 25

please note that the equation is different if the center isn't (0, 0)

Answer 3

for the first one, the center is (0, 0) and the radius is 4. x and y have nothing subtracted or added so it must be zero. The square root of 16 is 4, making the radius. and for the 2nd the equation is x^2+y^2=25 The 25 is from 5 squared, the x^2 is from (x-0)^2 and same with the y. I think thats right.

Answer 4

equation of a circle looks like
(x-a)^2 + (y-b)^2=r^2
a is horizontal shift
b is vertical shift
r is radius

simplified to your need is
y = sqroot(r^2-x^2)

because there is no a or b.

so solve for y

x^2 + y^2 = 16
y^2 = 16 - x^2

y = sqroot(16-x^2)

so that's the equation. r^2 = 16. sqrt(16) = 4 radius = 4

If the center is the origin that means you don't have to move it up or down. so a and b are 0 Back to the original equation

y = sqroot(r^2-x^2)

they gave you r so just plug it in and you get the equation:

y = sqroot(5^2-x^2)
y = sqroot(25-x^2)

Answer 5

set X or Y equal to zero, and plot the points on a graph.

If Y is zero, you would get points at X equal to plus and minus 4. If X is zero, you would get points at Y equal to plus and minus 4. Connect the dots and you have a circle centered at (0, 0) with a radius of 4.

if you follow the same logic you will find the answer to the second one... it will be in the form of X^2 + Y^2 = A

Draw it out and figure out what A is.

Answer 6

Well, not to preach, but...

...go to class.

The general circle equation is (x-a)^2 + (y-b)^2=r^2...it should be clear what a, b, and r represent...you can use this to do what you need to do.

Answer 7

That is why, no matter what you should show up for class.