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Question

What does the equation (ab)(x2+y2)2abx=0 become if the origin be moved to the point (abab,0)?

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Solution

(ab)(x2+y2)2abx=0..........(1)
Let a point on the curve with respect to origin be (x,y)
Let the same point with respect to new origin be (x,y)
The origin is moved from (0,0) to (abab,0)
Thus, x=x+abab and y=y
Putting the value of x and y in equation (1), we get
(ab)((x+abab)2+y2)2ab.(x+abab)=0
or, (ab)(x2+a2b2(ab)2+2xabab+y2)2abx2a2b2ab=0
Dividing both sides by (ab),
(x2+a2b2(ab)2+2xabab+y2)2xabab2a2b2(ab)2=0
or, x2+y2=a2b2(ab)2
or, (ab)2(x2+y2)=a2b2

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