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Prove the equation for the straight lines through the origin each of which makes an angle $\alpha$ with the straight line $y=x$.
Prove the equation for the straight lines through the origin each of which makes an angle $\alpha$ with the straight line $y=x$.
The equation is $x^2 - 2xy\sec^2\alpha + y^2 = 0$.
If the pair of straight lines is $x^2 - 2lxy - y^2 = 0$, show that the later pair also bisects the angle between the former.
If the pair of straight lines is $x^2 - 2lxy - y^2 = 0$, show that the later pair also bisects the angle between the former.
The later pair is given by $x^2 - 2mxy - y^2 = 0$, where $m = \frac{l^2}{2}$.
Find the separate equation of the following pair of straight lines: i) $3x^2 + 2xy - y^2 = 0, ii) 6(x-1)^2 + (x-1)(y-2) - 4(y-2)^2 = 0, iii) 2x^2 - xy - 3y^2 - 6x + 19y - 20 = 0
Find the separate equation of the following pair of straight lines: i) $3x^2 + 2xy - y^2 = 0, ii) 6(x-1)^2 + (x-1)(y-2) - 4(y-2)^2 = 0, iii) 2x^2 - xy - 3y^2 - 6x + 19y - 20 = 0
i) $x+y=0$, ii) $x-2y+6=0$, iii) $2x-3y-5=0$.
Find $p$ and $q$ if the following equation represents a pair of perpendicular lines: $6x^2 + 5xy - py^2 + 7x + qy - 5 = 0$
Find $p$ and $q$ if the following equation represents a pair of perpendicular lines: $6x^2 + 5xy - py^2 + 7x + qy - 5 = 0$
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For what value of $k$ does the equation $12x^2 + 2kxy + 2y^2 + 11x - 5y + 2 = 0$ represent two straight lines?
For what value of $k$ does the equation $12x^2 + 2kxy + 2y^2 + 11x - 5y + 2 = 0$ represent two straight lines?
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