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Area of the triangle formed by the lines...

Area of the triangle formed by the lines `y^2-9x y+18 x^2=0a n dy=6` is____

Text Solution

Verified by Experts

The correct Answer is:
3
We have
`y^(2)-9xy+18x^(2)=0`
or `y^(2)-6xy-3xy+18x^(2)=0`
or `y(y-6x)-3x(y-6x)=0`
or `y-3x=0andy-6x=0`
The third line is `y=6` . Therefore , the area of the triangle formed by these lines
`=(1)/(2)|{:(0,0,1),(1,6,1),(2,6,1):}|`
`=(1)/(2)|6-12|`
`=3"units"^(2)`
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