Question

the line (8x+3y-15) +
$\alpha$(3x-8y+2) =0 is parallel to X-axis . find $\alpha$

Answer 1

(8x + 3y - 15)+ α(3x - 8y + 2) = 0 is parallel to x - axis.

(8 + 3α)x + (3 - 8α)y + (-15 + 2α) = 0 is parallel to x - axis.
equation of x - axis is y = 0 or , 0.x + 1.y = 0

we know,
parallel of two lines means slope of lines are equal .
so, slope of 1st line = slope of 2nd line
-(8 + 3α)/(3 - 8α) =- 0/1 = 0
(8 + 3α) = 0
α = -8/3

hence, α = -8/3