Answer:
The equation of a straight line passing through the origin can be written in the form y = mx, where m is the slope of the line. To find the equation of a line that is perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line.
A line that is perpendicular to a line with the equation ax²-2hxy-by², we can find the slope of the given line by taking the derivative with respect to x.
The slope of the line is -2hy/ax.
The negative reciprocal of this slope is ax/2hy.
So the equation of the line perpendicular to ax²-2hxy-by² and passing through the origin is y = ax/2hy * x.
Note that if a = 0, the line is parallel to Y-axis and if b = 0, the line is parallel to X-axis.