Question

By translating the axes the equation ty – 27 – 3y – 4 = 0 has changed to XY = k then
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Answer 1

Answer:

Suppose the origin is shifted to (α,β).

Then x−α=X

and y−β=Y

Therefore x=X+α

∴y=Y+β

Hence, xy−2x−3y−4=0

(X+α)(Y+β)−2(x+α)−3(Y+β)−4=0

⇒XY+βX+αY+αβ−2X−2α−3Y−3β−4=0

⇒XY+X(β−2)+Y(α−3)+αβ−2α−3β−4=0

To make the linear terms disappear.

⇒β−2=0

⇒α−3=0

Hence, (α,β)=(3,2)

Thus the axes have to be translated along (3,2).

On substituting, we get

XY+6−2(3)−3(2)−4=0

⇒XY+6−6−6−4=0

⇒XY=10

Hence, k=10

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation: