Question

If straight lines 3x-5y=7 and 4x+ay+9=0 are perpendicular to one another . Find a

Answer 1

A question from ICSE 2018 Mathematics question paper.

Answer 2

Answer:

12/5

Step-by-step explanation:

Equation of line: y = mx+c  --a

$3x-5y=7$

Convert this line in the general from

$3x-7=5y$

$\frac{3x-7}{5}=y$

$\frac{3x}{5}-\frac{7}{5}=y$

Compare this with a

So, m = $\frac{3}{5}$

$4x+ay+9=0$

$ay=-4x-9$

$y= -\frac{4x}{a}-\frac{9}{a}$

Compare this with a

So, m = $\frac{-4}{a}$

Since we are given that  straight lines 3x-5y=7 and 4x+ay+9=0 are perpendicular to one another

So, it two lines are perpendicular then the product of their slopes is -1

⇒$\frac{-4}{a}\times\frac{3}{5} =-1$

⇒$\frac{12}{5}=a$

Hence the value of a is 12/5