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Question

All chords of the curve 3x2-y2-2x+4y = 0 that subtends a right angle at the origin, pass through a fixed point whose coordinates are


A
(1, −2)
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B
(1, 2)
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C
(-1, 2)
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D
(-1,- 2)
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Solution

The correct option is D (1, −2)
Let the equation of chord by y = mx + c. Combined equation of line joining the point intersection with origin is
3x2y22(x2y)(ymxc)=0i.e.,x2(3c+2m)y2(c4)2xy(1+2m)=0
These lines will be mutually perpendicular, if
3c + 2m – c + 4 = 0
2m + 2c = −4
m + c = −2
That means the chord y = mx + c is always pass through the point (1, −2).
Hence, (a) is the correct answer.

Mathematics

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