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Question

The equation of the line, passing through the centre and bisecting the chord 7x+y1=0 of the ellipse x21+y27=1, is

A
x7y=0
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B
7xy=0
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C
xy=0
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D
x+y=0
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Solution

The correct option is C xy=0

Given, equation of the ellipse is
x21+y27=1
Equation of chord QR with mid point at (h,k) is
T=S1
hx1+ky7=h21+k27 (1)
But given, equation of QR is
7x+y=1 (2)
Line (1) and (2) are identical
h7=k7h=k
Hence, equation of the line joining (0,0) and (h,k) is yx=0.

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