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Question

The equation of a chord of the circle x2+y23x4y4=0, which passes through the origin such that the origin divides it in the ratio 4:1, is

A
x=0
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B
24x+7y=0
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C
7x+24y=0
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D
7x24y=0
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Solution

The correct option is B 24x+7y=0
Then point of intersections are given by

x2(1+m2)x(3+4m)4=0

x1+x2=3+4m1+m2 and x1x2=41+m2

Since (0,0) divides the chord in the ratio 1:4,

x2=4x1

3x1=3+4m1+m2 and 4x21=41+m2

9+9m2=9+16m2+24m

i.e., m=0,247

Therefore, the lines are y=0 and 7y+24x=0.

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