SOLUTION: The equation of a curve xy = 12 and the equation of a line L is 2x + y = k, where k is a constant. i) In the case where k = 11, find the coordinates of the points of intersction

Question 1200186: The equation of a curve xy = 12 and the equation of a line L is 2x + y = k, where k is
a constant.
i) In the case where k = 11, find the coordinates of the points of intersction of L
and the curve.
ii) Find the set of values of & for which I does not intersect the curve.
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

I'll answer part (i) only.
Part (ii) seems a bit garbled so you'll need to revise.

Part (i)

Plug k = 11 into the 2nd equation and isolate y.
2x+y = k
2x+y = 11
y = -2x+11

Plug this into the other equation.
xy = 12
x(-2x+11) = 12
-2x^2+11x = 12
-2x^2+11x-12 = 0

Turn to the quadratic formula.
We'll plug in
a = -2
b = 11
c = -12

or

or

or

or

If x = 1.5, then,
y = -2x+11
y = -2*1.5+11
y = -3+11
y = 8
Making (1.5, 8) one point of intersection.

If x = 4, then,
y = -2x+11
y = -2*4+11
y = -8+11
y = 3
Making (4, 3) the other point of intersection.

Graph:

xy = 12 in green
2x+y = k in blue, where k = 11
1.5 = 3/2

Here's a more zoomed-out look of the graph.

I recommend using either Desmos or GeoGebra as a graphing tool.

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