Question

The circle x^2 + y^2 - 4x - 2y = 4 has two x-intercepts x1 and x2 as well as two y-intercepts y1 and y2. Verify the following:

Answer 1

@wio

Answer 2

a) x1 + x2 = 4

Answer 3

b) y1 + y2 = 2

Answer 4

c) |x1x2|=|y1y2|=4

Answer 5

@wio

Answer 6

help me @perl

Answer 7

please! ive been stuck for a long time

Answer 8

you can find the equation of a circle
(x-h)^2 + (y - k)^2 = r^2

Answer 9

i did that already

Answer 10

what do you have

Answer 11

the x intercepts occur when y = 0

Answer 12

i got (x-2)^2 + (y-1)^2 = 9

Answer 13

any ideas wio?

Answer 14

Well, when you have an \(x\) intercept \(x_1\), that means there is a point \((x_1,0)\).

Answer 15

So one thing you can do is plug in that point, I suppose.

Answer 16

into the equation of the circle?

Answer 17

Into the equation they gave you.

Answer 18

For example, for the point \((x_1,0)\), we have:\[
(x_1)^2 + (0)^2 - 4(x_1) - 2(0) = 4
\]

Answer 19

@Andrew12840 i got (x-2)^2 + (y-1)^2 = 9
are you sure its =9 and not = 10

Answer 20

ok so i got (a), is (b) the same thing?

Answer 21

its not working for b)

Answer 22

i get y^2-2y-4=0

Answer 23

Okay, I think you're a little confused

Answer 24

I'm basically thinking we solve for the intercepts.

Answer 25

\[
x^2 + y^2 - 4x - 2y = 4
\]If we let \(y=0\), then: \[
x^2-4x-4=0
\]Using the quadratic formula will give use our result.

Answer 26

It will give us our two intercepts

Answer 27

i understand that im talking about problem b) y1+y2=2

Answer 28

For that we'd have: \[
y^2-2y-4=0
\]

Answer 29

thats what i got

Answer 30

where do i go from there

Answer 31

what did you get for the roots?

Answer 32

1 plus or minus rad 5

Answer 33

got the same

Answer 34

Add and you will get \(2\).

Answer 35

The \(\pm\) part cancels out

Answer 36

what?

Answer 37

b) verify y1 + y2 = 2
left hand side
y1 = 1 + rad 5 and y2 = 1 - rad 5
y1 + y2 = 1 + rad 5 + 1 - rad 5 = 2 = right hand side

Answer 38

oh ok

Answer 39

do you know how to do c)?

Answer 40

repost it here

Answer 41

c) |x1x2|=|y1y2|=4

Answer 42

i have to verify it

Answer 43

Since you already know all the intercepts, just plug it in.

Answer 44

thanks to both of you

Answer 45

you are welcome