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# Maths Circle Problem watch

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1. I'm really stuck on this maths question and don't know how to work it out. The question is y= -3x+c is a tangent to the circle x^2+y^2-4x-2y-5=0. Find c. Can anyone help? Thanks
2. (Original post by issyafd1)
I'm really stuck on this maths question and don't know how to work it out. The question is y= -3x+c is a tangent to the circle x^2+y^2-4x-2y-5=0. Find c. Can anyone help? Thanks
Substitute y=x+c into the equation of the circle and rearrange to get a quadratic equation set to 0.
Then as the line is a tangent to the curve, the discriminant will be 0. So if you do b^2 -4ac which is the discriminant and set it =0 you will form a quadratic in terms of c and so you can then solve.
3. thank you so much :-). I subbed the equation of a line into the equation of the circle and got 10x^2-6cx+c^2+2x+c-5 but am not sure what would be a,b,c?
4. (Original post by issyafd1)
thank you so much :-). I subbed the equation of a line into the equation of the circle and got 10x^2-6cx+c^2+2x+c-5 but am not sure what would be a,b,c?
If you factorise for each term x^2, x and the constant term, you would get (assuming what you have written is correct) 10x^2 +2(1-3)x+c^2+c-5=0
5. Thank You
So would a be 10x^2, b be 2(1-3)x and c be c^2+c-5 ?
6. (Original post by issyafd1)
Thank You
So would a be 10x^2, b be 2(1-3)x and c be c^2+c-5 ?
Yes.
7. Thank you so much :-)
8. (Original post by issyafd1)
Thank you so much :-)
What did you get for the equation of the tangents in the end?
9. (Original post by issyafd1)
I'm really stuck on this maths question and don't know how to work it out. The question is y= -3x+c is a tangent to the circle x^2+y^2-4x-2y-5=0. Find c. Can anyone help? Thanks
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