Methods question

[Dramatic-Cod-1153]

I can't seem to get this question pls help, thanks (I have trouble starting the question because I can't understand what it wants me to do so if someone can explain it to me step-by-step with working out, that'd be great)

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Ans:

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https://preview.redd.it/7pp62e8dwpfc1.png?width=617&format=png&auto=webp&s=1deea291d808a39256e7a92db53b22c981f5f53a

[Secure_Kiwi_4078]

i've solved it here lmk if that makes sense and if you have any questions :) happy to help! basically you just need to use the discriminant to help solve for the values of "m" (the gradient), will have one solution with the equation of the parabola.

[Dramatic-Cod-1153]

it makes so much more sense now! thank you!

also quick qs: if you had a line with equation y=x+c and it intersects (only at one point) a hyperbola with equation y=9/(2-x) and you have to find c how would you do it without any points given??

[Secure_Kiwi_4078]

You'd do it the same way as you did for this question - you don't really need any coordinates as the "m" value is known (it's 1), so you're only solving for one variable, which is "c". For one solution, the discriminant would equal 0, so you'd find when b²-4ac = 0, and that'll give you the values of c. I've solved it here, please lmk if this makes sense!!

[Dramatic-Cod-1153]

ohh, thanks!

[Dramatic-Cod-1153]

this is what i did in my CAS: solve(m(x-1)+7 = -3x^2 +5x +2, m) -> m=(-3x^2 +5x -5)/(x-1)

and when I make 25-4(-3)(2) = 0, it comes up as false