Question

For what values of a and b the intercepts cuts off on the coordinate axes by the line ax+by+8=0 are equal in length and same signs to those cut off by the line 2x-3y+6=0 on the axes

Answer 1

Answer:

$a =\frac{8}{3}$ and b = - 4.

Step-by-step explanation:

The equation of the given straight line is 2x - 3y + 6 = 0

So, the equation can be rearranged to  

2x - 3y = - 6

⇒ $\frac{2x}{-6} - \frac{3y}{-6} = 1$

⇒$\frac{x}{-3} + \frac{y}{2} = 1$.

So, the x-intercept is -3 and the y-intercept is 2.

Now, given the unknown equation ax + by + 8 = 0

This equation can be rearranged to ax + by = - 8

⇒ $\frac{x}{\frac{-8}{a} } + \frac{y}{\frac{-8}{b} } = 1$  

It is given that the intercepts cuts off on the coordinate axes by the line ax+by+8=0 are equal in length and same signs to those cut off by the line 2x-3y+6=0 on the axes.

Therefore, $\frac{-8}{a} = -3$

⇒ $a =\frac{8}{3}$ (Answer)

Again, $\frac{-8}{b} = 2$

⇒ b = - 4 (Answer)

Answer 2

Answer:

a=-8/3 and b=4

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