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as level maths coordinate geometry🤞🤞

a line has equation 2x+y=20 and the curve has equation y=a+18/x-3, where a is a constant.
find the set of values of A for which the line does not intersect the curve.
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Avatar for harrydjb
harrydjb
4
Set the y's of the equations equal, mulitiply by the denominator x-3. Factor by grouping to work with the discriminant >= 0 since they must touch at least one place. Next complete the square on the resulting quadratic formed by using the discriminant. :smile:
A is constant so it should be included in the equation
just plz solve the sum, i have many other sums also
Original post by shah kaivan
just plz solve the sum, i have many other sums also


We're not here to solve your problems for you.

Have a go yourself, you got told the method. Equate the y's to get an equation in x and a that describes the points of intersection; you can manipulate it into a quadratic. The question says these dont intersect so the equation has no solutions in x. This means the discriminant (which is entirely in terms of a) is negative. So this yields an inequality in a for you to solve, do it.
(edited 4 years ago)
20-2x=a+18/x-3
Original post by shah kaivan
20-2x=a+18/x-3


When you write that it's impossible for the other person to know whether the RHS says

a+18x−3a+\dfrac{18}{x} - 3

or a+18x−3\dfrac{a+18}{x}-3

or a+18x−3\dfrac{a+18}{x-3}

or a+18x−3a+\dfrac{18}{x-3}


Anyhow, whichever one it is, just multiply the entire equation through by the denominator and you end up with the quadratic... then follow along the advice said in my last post.
so what is ans
Original post by shah kaivan
so what is ans


You’ve been given the ingredients, now use them to solve the question.
Reply 9
Avatar for harrydjb
harrydjb
4
Sorry man misread thought it said does intersect my bad.

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