The angle between lines joining origin a...

The angle between lines joining origin and intersection points of line `2x+y=1` and curve `3x^2+4yx-4x+1=0`, is

`(pi)/2`

`(pi)/3`

`(pi)/4`

`(pi)/6`

Text Solution

Verified by Experts

The correct Answer is:

The equation of required line is
`3x^(2)+4xy-4x(2x+y)+(2x+y)^(2)=0`
`implies3x^(2)+4xy-8x^(2)-4xy+4x^(2)`
`+y^(2)+4xy=0`
`implies-x^(2)+y^(2)+4xy=0`
`("Coefficient of" x^(2))+("Coefficient of" y^(2))`
`=-1+1=0`
Hence, lines are mutually perpendicular.
i.e. Angle between lines is `(pi)/2`

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