The length of the perpendicular(s) from the origin to the line passing through (2,2) and perpendicular to the linesx2+2xy−3y2=0, is/are
A
2√2√5 units
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B
2√5 units
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C
2√2 units
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D
2 units
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Solution
The correct option is C2√2 units Given curve: x2+2xy−3y2=0 ⇒x2+3xy−xy−3y2=0 ⇒(x+3y)(x−y)=0
So, lines will be x+3y=0 or x−y=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=2√2 units
Now for line x+3y=0 the perpendicular line will be 3x−y=4
so distance from the origin =|−4|√10=2√2√5 units