The equation of the line, passing through the centre and bisecting the chord 7x+y−1=0 of the ellipse x21+y27=1, is
A
x−7y=0
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B
7x−y=0
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C
x−y=0
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D
x+y=0
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Solution
The correct option is Cx−y=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=k7⇒h=k Hence, equation of the line joining (0,0) and (h,k) is y−x=0.