Problem :
How to find the equation of lines passing through the origin and perpendicular to the lines $xy-3y^2+y-2x+10=0$
My working on this :
Two lines are perpendicular if the sum of coefficient of $x^2$ and $y^2$ is equal to zero.
[Math] How to find the equation of lines passing through the origin and perpendicular to the lines $xy-3y^2+y-2x+10=0$
coordinate systems
Related Question
- [Math] Equation of a straight line passing through passing through a point and equally inclined to two other lines
- [Math] Equation of a pair of straight lines through the origin and passing through the intersection of two curves
- Finding all Lines Passing Through a Point Given the Product of Intercepts
- Line through two given skew lines and origin
Best Answer
HINT:
$$3y^2-y(x+1)+2x-10=0$$
$$y=\frac{x+1\pm\sqrt{(x+1)^2-12(2x-10)}}{2\cdot3}=\frac{x+1\pm\sqrt{x^2-22x+121}}6=\frac{x+1\pm(x-11)}6$$
Can you determine the gradients from here and reach the destination?