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# CIRCLE QUESTION-help needed watch

1. The line with equation mx-y-2=0 touches the circle with equation x^2+6x+y^2-8y=4. Find 2 possible values of m, giving your answers in exact form.

I worked it out but i can't find the mark scheme to this worksheet. Can someone please answer it and check with me?

I got 9+2root29 over 10 AND 9 - 2root29 over 10
2. Try the app “Socratic” if you’re stuck with maths, I find it really helpful
3. (Original post by Mark jam)
The line with equation mx-y-2=0 touches the circle with equation x^2+6x+y^2-8y=4. Find 2 possible values of m, giving your answers in exact form.

I worked it out but i can't find the mark scheme to this worksheet. Can someone please answer it and check with me?

I got 9+2root29 over 10 AND 9 - 2root29 over 10
This is correct. (though it should be 'OR' and not 'AND')
4. Solving the simultaneous eqns, (sub y=mx-2 into quadratic), you get

x^2(1+m^2) + x(6-12m) + 16 = 0

Now use property of discriminant for this eqn: since the straight line is a tangent for each value of m, there is only one solution to this quadratic, (some say repeated roots); hence the discriminant for this quadratic is equal to zero.

This gives

80m^2 - 144m - 28 = 0
which doesn't factorise, so completing the square, (or using the formula) gives

m= 9/10 +/- 2root(29)/10

Never certain about whether this is m = .... AND m = .... or m=... OR m=...
I usually write a comma in between the answers ....

hth

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Updated: March 10, 2018
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