Question

Find the equation of a pair of lines passing through the point (1,0) and parallel to the lines represented by the equation 3x^2 + xy - 10y^2.

Answer 1

Answer:

$y=\frac{3}{5} x-\frac{3}{5}$

$y=-\frac{1}{2} x+\frac{1}{2}$

Step-by-step explanation:

The equation will form two lines because

the factorization is $(3x-5y)(x+2y)$.

Each factors form a line.

Therefore, two lines are $3x-5y=0$ and $x+2y=0$.

The slopes of each lines are $\frac{3}{5}$ and $-\frac{1}{2}$ respectively.

First equation will be $y-0=\frac{3}{5} (x-1)$.

The other will be $y-0=-\frac{1}{2} (x-1)$.

Answer

$y=\frac{3}{5} x-\frac{3}{5}$

$y=-\frac{1}{2} x+\frac{1}{2}$