Question

The equation of a curve is xy=12 and the equation of line 3x+y=k, where k is constant. In the case where k=20, the line intersects the curve at the points A and B.
a) What is the midpoint of the line AB?
b) What is the set of values of k which the line 3x+y=k intersects the curve at two distinct points?

Answer 1

Answer:

tan[a-b]=tan z =[ m (I) -m(T)]/[1+m(I).m(T)] ,where z is the angle between the two lines.

M(I) = -2 So find m(T)

xy=12

d{xy]/dx=0

x dy/dx +y=0

The slope of any tangent to the curve is m(T) = dy/dx = -y/x

At [x,y] = [2,6]

m(T) = - 6/2=-3

tan z=|[(-2+3 )/(1+6)]| =|1/7|

The two angles between I and T are arc tan(1/7) and arc tan(-1/7)

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

can you please repeat the ans?