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c2 circles help (new kid)

hi there ppl

i have question!

show that the circle x^2 + y^2 - 2ax - 2bx + b^2 = 0 touches y-axis

thnax :smile:
Reply 1
Avatar for lolman42
lolman42
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any 1?:smile:
Original post by lolman42
hi there ppl

i have question!

show that the circle x^2 + y^2 - 2ax - 2bx + b^2 = 0 touches y-axis

thnax :smile:



Assuming that it's 2by ,you need to show that the line x=0 is a tangent to the circle.

So set x equal to zero and observe the nature of the resulting quadratic in y.

Hint:

for a tangent,

b2=4acb^2 = 4ac
Reply 3
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lolman42
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Original post by Indeterminate
Assuming that it's 2by ,you need to show that the line x=0 is a tangent to the circle.

So set x equal to zero and observe the nature of the resulting quadratic in y.

Hint:

for a tangent,

b2=4acb^2 = 4ac

but the resulting quadratic has a b^2 term and a y^2 term after setting the x's to zero in the circle equation
Reply 4
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lolman42
OP
Original post by Indeterminate
Assuming that it's 2by ,you need to show that the line x=0 is a tangent to the circle.

So set x equal to zero and observe the nature of the resulting quadratic in y.

Hint:

for a tangent,

b2=4acb^2 = 4ac


I am unsure still :/
Original post by lolman42
but the resulting quadratic has a b^2 term and a y^2 term after setting the x's to zero in the circle equation


Are you sure you've not made a mistake in copying out the Q?

Otherwise, when we're on the y-axis

y2+b2=0y^2 + b^2 =0

which is impossible.
Reply 6
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lolman42
OP
Original post by Indeterminate
Are you sure you've not made a mistake in copying out the Q?

Otherwise, when we're on the y-axis

y2+b2=0y^2 + b^2 =0

which is impossible.


yep this is it: x^2 + y^2 - 2ax - 2bx + b^2 = 0

I have triple checked :P
Reply 7
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lolman42
OP
Original post by Indeterminate
Are you sure you've not made a mistake in copying out the Q?

Otherwise, when we're on the y-axis

y2+b2=0y^2 + b^2 =0

which is impossible.


what shall I do? :/
Reply 8
Avatar for davros
davros
16
Original post by lolman42
yep this is it: x^2 + y^2 - 2ax - 2bx + b^2 = 0

I have triple checked :P


so there isn't a 'y' term but there are 2 'x' terms: -2ax and -2bx?
Reply 9
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lolman42
OP
Original post by davros
so there isn't a 'y' term but there are 2 'x' terms: -2ax and -2bx?

Yeap- I have checked meticulously

It's exactly how it is in my book
Reply 10
Avatar for davros
davros
16
Original post by lolman42
Yeap- I have checked meticulously

It's exactly how it is in my book


I think the question must be wrong then... as pointed out earlier, when x=0 you have y^2 + b^2 = 0 which is impossible!
Reply 11
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lolman42
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Original post by davros
I think the question must be wrong then... as pointed out earlier, when x=0 you have y^2 + b^2 = 0 which is impossible!

Yeh, I thought that.. thanks bud :smile:
Original post by lolman42
hi there ppl

i have question!

show that the circle x^2 + y^2 - 2ax - 2bx + b^2 = 0 touches y-axis

thnax :smile:


Certainly an error in your book

The question should read

x2+y2−2ay−2bx−b2=0x^2 + y^2 - 2ay - 2bx - b^2 = 0

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