Question

The equation of a curve is xy=12 and the equation of a line L is 2x+y=k where k is a constant.
I) in the case k=11 find the coordinates of the points of intersection of L and the curve.
Ii) find the set of values of k for which L does not intersect the curve.
Iii) in the case where k=10 one of the points of intersection is p(2,6). Find the angle in degrees between L and the tangent to the curve at P

Answer 1

y = 12 / x
2x + y = 11

2x + ( 12 / x ) = 11
2x^2 - 11x + 12 = 0
(2x - 3 ) ( x - 4 ) = 0
x = 3 /2, y = 8 or x = 4, y = 3

Answer 2

I solves I but iam stuck on both ii and iii and thank you

Answer 3

Solved i*

Answer 4

Should I differentiate

Answer 5

And k is not equal to 11

Answer 6

When I looked back to my textbook answer appears to be 9.8 and -9.8

Answer 7

ii)
y = 12/x
2x+y =k
replace y to second one you have 2x^2 +12-kx =0
discriminant <0 --> no solution
so (-k)^2 -4*2*12 <0
k^2 <96
-9.8< k <9.8

Answer 8

a little bit faster, :)

Answer 9

Thank you so so much but why is m=3

Answer 10

Oh now I understand thank you man

Answer 11

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