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Find the angle between the straight line...

Find the angle between the straight lines joining the origin to the point of intersection of `3x^2+5x y-3y^2+2x+3y=0` and `3x-2y=1`

Text Solution

Verified by Experts

The correct Answer is:
`pi//2`
The equation of the line is
`3x-2y=1` (1)
and the equation of the curve is
`3x^(2)+5xy-3y^(2)+2x+3y=0` (2)
Making (2) homogenous with the help of (1), we get
`3x^(2)+5xy-3y^(2)+(2x+3y)(3x-2y)=0`
or `9x^(2)+10xy-9y^(2)=0` (3) which is the equation of the lines joining the origin to the point of intersection of (1)and (2).
Here ,` a=9,b=-9`.
Since a+b=0, the two lines given by (3) are at right angles .
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