Question

The sum of the slopes of the lines represented by $12x^2-20xy+7y^2=0$ is

• A. $-\frac{1}{3}$
• B. $\frac{12}{7}$
• C. $\frac{2}{3}$
• D. $\frac{20}{7}$

Answer 1

Answer: (D)

$\frac{20}{7}$

The general form is like this

$a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$

Only concentrate on the 2 degree terms,

$a{x}^2+2hxy+b{y}^2$ = 0

These terms contain information about the slope of both the lines. And in fact this is also a pair of straight lines which is same as before but only their intersection point is origin.

Divide by $x^2$, u get:

a +$2h\left(\frac{y}{x}\right)+b(\frac{y}{x}{)}^2=0$

This is a quadratic equation in y/x and we get the 2 slope values of both the lines.

For given ques. ,we have , on diving by $x^2$

$12-20\frac{y}{x}+7{\left(\frac{y}{x}\right)}^2=0$

on solving above quadratic eqn in $\frac{y}{x}$,we get

$\frac{y}{x}=\frac{14}{7},\frac{6}{7}$, they are the slopes of respective pair of lines.

So, sum of these is $\frac{20}{7}$