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Question

The length of the perpendicular(s) from the origin to the line passing through (2,2) and perpendicular to the linesx2+2xy3y2=0, is/are

A
225 units
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B
25 units
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C
22 units
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D
2 units
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Solution

The correct option is C 22 units
Given curve: x2+2xy3y2=0
x2+3xyxy3y2=0
(x+3y)(xy)=0
So, lines will be
x+3y=0 or xy=0
Now
Equation of normal to x=y and passes through (2,2) will be x+y=4
so distance from the origin =|4|2=22 units
Now for line x+3y=0 the perpendicular line will be 3xy=4
so distance from the origin =|4|10=225 units

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