Question

Transform the line x + y - 1 = 0 to the parallel axes through the point (1, 0).​

Answer 1

Transform to parallel axes through the point (1,−2) the equations

(1) y

2

−4x+4y+8=0,

and (2) 2x

2

+y

2

−4x+4y=0.

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ANSWER

(1)y

2

−4x+4y+8=0...........(1)

Let the point on the curve with respect to old axis is (x,y)

Let the same point on the curve with respect to new axis be (x

′

,y

′

)

The new co-ordinates are shifted by (1,−2)

Thus x=x

′

+1 and y=y

′

−2

Replacing the value of x and y in (1),we get

(y

′

−2)

2

−4(x

′

+1)+4(y

′

−2)+8=0

or, y

′2

+4−4y

′

−4x

′

−4+4y

′

−8+8=0

or, y

′2

=4x

′

(2)2x

2

+y

2

−4x+4y=0..........(2)

Let the point on the curve with respect to old axis is (x,y)

Let the same point on the curve with respect to new axis be (x

′

,y

′

)

The new co-ordinates are shifted by (1,−2)

Thus x=x

′

+1 and y=y

′

−2

Replacing the value of x and y in (2),we get

2(x

′

+1)

2

+(y

′

−2)

2

−4(x

′

+1)+4(y

′

−2)=0

or, 2(x

′2

+1+2x

′

)+(y

′2

+4−4y

′

)−4x

′

−4+4y

′

−8=0

or, 2x

′2

+2+4x

′

+y

′2

−4x

′

−8=0

or,2x

′2

+y

′2

=6