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Tangent to a circle

The circle C has equation x2 - 8x +y2 - 4y +15. A line is a tangent to a circle if it touches it once only (rather than intersecting it twice or not touching it at all). Use this information to show that l is a tangent to C.

l= 2x-y-1=0
Reply 1
Avatar for TenOfThem
TenOfThem
18
Original post by 50ShadesOfRay
The circle C has equation x2 - 8x +y2 - 4y +15. A line is a tangent to a circle if it touches it once only (rather than intersecting it twice or not touching it at all). Use this information to show that l is a tangent to C.

l= 2x-y-1=0


Get y=
Substitute
Solve

Point out that there is only one answer
Reply 2
Avatar for 50ShadesOfRay
50ShadesOfRay
OP
Original post by TenOfThem
Get y=
Substitute
Solve

Point out that there is only one answer


it just says show that, it doesn't give an answer, i tried multiplying out, but i don't think it's that complicated?
Reply 3
Avatar for TenOfThem
TenOfThem
18
Original post by 50ShadesOfRay
it just says show that, it doesn't give an answer,



of course

i tried multiplying out, but i don't think it's that complicated?


Not sure what you mean by this

Did you understand what I said in my previous post
Reply 4
Avatar for 50ShadesOfRay
50ShadesOfRay
OP
Original post by TenOfThem
of course



Not sure what you mean by this

Did you understand what I said in my previous post


not at all haha
Reply 5
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TenOfThem
18
Original post by 50ShadesOfRay
not at all haha


So, what have you tried "multiplying out"
Reply 6
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50ShadesOfRay
OP
Original post by TenOfThem
So, what have you tried "multiplying out"


i rearranged L for y

subbed into the whole circle equation

got a massive equation
which i simplified

and i needed the quadratic equation to solve after i simplified, what have i achieved?
Reply 7
Avatar for TenOfThem
TenOfThem
18
Original post by 50ShadesOfRay
i rearranged L for y

subbed into the whole circle equation

got a massive equation
which i simplified

and i needed the quadratic equation to solve after i simplified, what have i achieved?


That was what I said to do :smile:

How do you show that a quadratic has only one solution
Reply 8
Avatar for 50ShadesOfRay
50ShadesOfRay
OP
Original post by TenOfThem
That was what I said to do :smile:

How do you show that a quadratic has only one solution


sorry my minds blanked i have no clue
Reply 9
Avatar for TenOfThem
TenOfThem
18
Original post by 50ShadesOfRay
sorry my minds blanked i have no clue


You need to have a good understanding of the basic principles else you will not be able to attempt exam questions

You need to consider b2−4acb^2 - 4ac
Reply 10
Avatar for 50ShadesOfRay
50ShadesOfRay
OP
Original post by TenOfThem
You need to have a good understanding of the basic principles else you will not be able to attempt exam questions

You need to consider b2−4acb^2 - 4ac


Does the discriminant = 0?
Original post by 50ShadesOfRay
Does the discriminant = 0?


yes
Reply 12
Avatar for Secret.
Secret.
14
Original post by 50ShadesOfRay
Does the discriminant = 0?



If the discriminant equals 0 then your quadratic has one (repeated) solution

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