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C2- Circle geometry

Can someone assist me with the following question:

The line with equation 2x+3y=k is a tangent to the circle with equation x2+y2+6x+4y=0x^2+y^2+6x+4y=0 Find the two possible values for k.

Don't know where to start :s-smilie:. Any hints on what to do first?
Original post by Super199
Can someone assist me with the following question:

The line with equation 2x+3y=k is a tangent to the circle with equation x2+y2+6x+4y=0x^2+y^2+6x+4y=0 Find the two possible values for k.

Don't know where to start :s-smilie:. Any hints on what to do first?


Draw a diagram, find the center and normal.

Posted from TSR Mobile
Reply 2
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the bear
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rewrite the circle equation in the form

(x - a)2 + (y - b)2 =r2
Reply 3
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Super199
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Original post by majmuh24
Draw a diagram, find the center and normal.

Posted from TSR Mobile


Original post by the bear
rewrite the circle equation in the form

(x - a)2 + (y - b)2 =r2


(x+3)2+(y+2)2=13(x+3)^2+(y+2)^2=13?
So centre (-3,-2)
Reply 4
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the bear
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Original post by Super199
(x+3)2+(y+2)2=13(x+3)^2+(y+2)^2=13?
So centre (-3,-2)


good !!

now find the gradient of the straight line
Reply 5
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Super199
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Original post by the bear
good !!

now find the gradient of the straight line

Is that the gradient of 2x+3y=k? So gradient = -2/3?
Reply 6
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games211
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Original post by Super199
Is that the gradient of 2x+3y=k? So gradient = -2/3?


can't you find the equation for the radius to the tangent and make that equal to the equation of the tangent line?
Reply 7
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Super199
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Original post by games211
can't you find the equation for the radius to the tangent and make that equal to the equation of the tangent line?

I was thinking that. What is the equation of the normal though? The gradient is 3/2 I presume as it is perpendicular to tangent but what point does it go through?
Reply 8
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games211
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Original post by Super199
I was thinking that. What is the equation of the normal though? The gradient is 3/2 I presume as it is perpendicular to tangent but what point does it go through?


isnt it the midpoint?
Reply 9
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Super199
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Original post by games211
isnt it the midpoint?

Midpoint of what?
Reply 10
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games211
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Original post by Super199
Midpoint of what?


the circle lol think my talking rubbish sorry lol
Reply 11
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Super199
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Original post by games211
the circle lol think my talking rubbish sorry lol

So the centre lmao?
Reply 12
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games211
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Original post by Super199
So the centre lmao?


yh sorry meant the centre. Im so dumb. Im doing it wrong sorry
Reply 13
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Super199
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Original post by games211
yh sorry meant the centre. Im so dumb. Im doing it wrong sorry

I've figured it out it's cool. You have to use the discriminant
Reply 14
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games211
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Original post by Super199
I've figured it out it's cool. You have to use the discriminant


lol what do you mean?
Reply 15
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Super199
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Original post by games211
lol what do you mean?

A tangent touches the circle at one point. so b2−4ac=0b^2-4ac=0
You are given the equation of the line 2x+3y=k.
You can either find an expression in terms of x or y. Then sub back in to the original equation and you should get quite a meaty quadratic.
Then solve it from there
Reply 16
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games211
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Original post by Super199
A tangent touches the circle at one point. so b2−4ac=0b^2-4ac=0
You are given the equation of the line 2x+3y=k.
You can either find an expression in terms of x or y. Then sub back in to the original equation and you should get quite a meaty quadratic.
Then solve it from there


thank you! got it!
(edited 10 years ago)
Reply 17
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Super199
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Original post by games211
thank you! got it!

Sub it into the equation of the circle given. I used x but should do the same stuff

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