geometry questions can ne one help!?

Question

1. Which of the following pieces of information are necessary to write the equation of any circle?


A.
an x-intercept and a y-intercept

B.
radius and the coordinates of the center

C.
coordinates of the center and intercepts

D.
radius and intercepts

2. Identify the intercepts of the circle (x - 5)^2 + (y + 12)^2 = 169.


A.
(0, 0), (10, 0), and (0,-24)

B.
(0, 0), (0, 10), and (-24, 0)

C.
(0, 0), (-10, 0), and (0, 24)

D.
(0, 0), (0,-10), and (24, 0)


How many y-intercepts does the circle x^2 + (y - 2)^2 = 16 have?


A.
0

B.
2

C.
3

D.
4

I think I know a couple of these but just to be on the safe side I need your ppls help! Please and thankyou!

Answer 1

1. B
2. A
3. B

Answer 2

1. Which of the following pieces of information are necessary to write the equation of any circle?


A.
an x-intercept and a y-intercept

Think about a plot of a circle, cutting the X and Y axis at some point. Can you imagine another circle cutting the X and Y axes at the same points? So, not A

B.
radius and the coordinates of the center
IF you want to draw a circle, then having the center and the radius would let you. Good candidate.


C.
coordinates of the center and intercepts
Also a good candidate, but wait, does a circle have to intercept the X and Y axes? If it does not you are just left with the center which is not enough information.

D.
radius and intercepts
Same as C


So the only definite one is B.



2. Identify the intercepts of the circle (x - 5)^2 + (y + 12)^2 = 169.

A. (0, 0), (10, 0), and (0,-24)
B. (0, 0), (0, 10), and (-24, 0)
C. (0, 0), (-10, 0), and (0, 24)
D. (0, 0), (0,-10), and (24, 0)

if x=0, then (0-5)^2 + (y+12)^2 = 169 expands to:
25+ y^2 +24y +144 = 169 Simplifies to
y^2 + 24y = 0

So, y=0, or y^2 = -24y divide both sides by y y=-24

so we have (0,0) and (0,-24)

The answer must be A




How many y-intercepts does the circle x^2 + (y - 2)^2 = 16 have?

A. 0
B. 2
C. 3
D. 4

What happens when x=0 ?
0^2 +(y-2)^2 = 16
so y-2 = sqrt(16) = +4 or -4
so y=6 or -2
so there are two itercepts on the X axis.

What happens if Y=0?

x^2 +(-2)^2 = 16
so x^2 + 4 = 16
so x^2 =12
x = sqrt(12)
this is plus or minus 3.something, but there are two intercepts.

So 2 on the x axis, 2 on the y, no common point at (0,0)

Answer D.

Answer 3

1. (B) - radius and the coordinates of the center - it is possible to have a circle with no intercepts, so the value of the intercepts does not define a circle

2. (A) - (0, 0), (10, 0), and (0,-24)
To find the x-intercepts, set x = 0 and solve for y.
To find the y-intercepts, sety y = 0 and solve for x.

3. (D) - 4
To find the x-intercepts, set x = 0 and solve for y.
To find the y-intercepts, sety y = 0 and solve for x.

Answer 4

man, y'all are doin' it wrong!! I'm doing this exact same thing in geometry right now. You're righting standard equations for circles right?
Okay, so here's the equation:
(x-h)^2 + (y-k)^2 = r^2

So here are your answers:

1. B

2. A

3. B

Answer 5

i'm sorry i don't know much about circles use a graphing calculator

Answer 6

That is more than one question.