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

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?

Please elucidate

Please elucidate

hi, i just did this question on integral as a homework 😂 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 would’ve gotten 100%, what does it matter anyway, they both mean the same thing!! 😤😤😤 lmao i’m so annoyed for no reason

hi, i just did this question on integral as a homework 😂 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

thanks, that really helped me understand how to do it.