# The line does not intercept the circle - find the range of values...

Hi,

Here is the question:

The line y=2x does not meet the circle (x-2)Â²+(y-1)Â²=d. Find the range of possible values for d.

I can't work out how to start!
Substitute y=2x into equation of the circle. This forms a quadratic in x. Now if the line and circle do not intersect then how many roots should this equation have?

Spoiler

Original post by B_9710
Substitute y=2x into equation of the circle. This forms a quadratic in x. Now if the line and circle do not intersect then how many roots should this equation have?

Spoiler

Original post by Grade9girl

Note that this thread is a year old

Substituting the equation of the line into the equation of the circle gives you a quadratic equation in x. If the line does not intersect the circle, then the equation must have no real roots. Which property of a quadratic equation tells you about the types of roots it has?
Original post by Grade9girl

hi, i just did this question on integral as a homework ðŸ˜‚ and i was stuck on it as well so i searched the question up and found ur thread. I know how to do it now so i thought I'd reply to ur question. I don't really know if you need it anymore tho

so..
sub y=2x into the equation of the circle:
(x-2)^2+(2x-1)^2=d...
that becomes..5x^2-8x+5=d

Now basically what we have is a quadratic and since the circle doesn't intrsect the line y=2x we use b^2-4ac<0
but before u do this you need to take d to the other side so that c becomes (5-d):
5x^2-8x+5=d
5x^2-8x+(5-d)=0

now substitute ur a b and c values into b^2-4ac<0:
(-8)^2-4*5*(5-d)<0
that becomes... 64-100+20d<0
rearrange and you get... d<1.8
Original post by silverbullet786
hi, i just did this question on integral as a homework ðŸ˜‚ and i was stuck on it as well so i searched the question up and found ur thread. I know how to do it now so i thought I'd reply to ur question. I don't really know if you need it anymore tho

so..
sub y=2x into the equation of the circle:
(x-2)^2+(2x-1)^2=d...
that becomes..5x^2-8x+5=d

Now basically what we have is a quadratic and since the circle doesn't intrsect the line y=2x we use b^2-4ac<0
but before u do this you need to take d to the other side so that c becomes (5-d):
5x^2-8x+5=d
5x^2-8x+(5-d)=0

now substitute ur a b and c values into b^2-4ac<0:
(-8)^2-4*5*(5-d)<0
that becomes... 64-100+20d<0
rearrange and you get... d<1.8

thank you!!! idk if they other person still needed it but i certainly did haha

i just did the same integral test and i entered the answer as a decimal instead of fraction and missed one mark, i wouldâ€™ve gotten 100%, what does it matter anyway, they both mean the same thing!! ðŸ˜¤ðŸ˜¤ðŸ˜¤ lmao iâ€™m so annoyed for no reason
Original post by weran
thank you!!! idk if they other person still needed it but i certainly did haha

i just did the same integral test and i entered the answer as a decimal instead of fraction and missed one mark, i wouldâ€™ve gotten 100%, what does it matter anyway, they both mean the same thing!! ðŸ˜¤ðŸ˜¤ðŸ˜¤ lmao iâ€™m so annoyed for no reason

ðŸ˜‚ðŸ˜‚ lol definitely made that mistake before!!! dont worry i only got 1/3!!! I suppose that means you take A-level maths. Dont wprry were in the same boat ðŸ˜…ðŸ˜…ðŸ˜…
(edited 3 years ago)
thanks
(edited 3 years ago)
thanks, that really helped me understand how to do it.

Original post by Zahra575!
hi, i just did this question on integral as a homework ðŸ˜‚ and i was stuck on it as well so i searched the question up and found ur thread. I know how to do it now so i thought I'd reply to ur question. I don't really know if you need it anymore tho

so..
sub y=2x into the equation of the circle:
(x-2)^2+(2x-1)^2=d...
that becomes..5x^2-8x+5=d

Now basically what we have is a quadratic and since the circle doesn't intrsect the line y=2x we use b^2-4ac<0
but before u do this you need to take d to the other side so that c becomes (5-d):
5x^2-8x+5=d
5x^2-8x+(5-d)=0

now substitute ur a b and c values into b^2-4ac<0:
(-8)^2-4*5*(5-d)<0
that becomes... 64-100+20d<0
rearrange and you get... d<1.8
I know we shouldn't revive old threads (to admin, sorry about commenting even more), but this is proof maths questions are timeless lol

Original post by 1-1AR31-1
thanks, that really helped me understand how to do it.