Find the equation of the lines which cut-off intercepts on the axes wh

1.	Find the equation of the lines which cut-off intercepts on the axes whose sum and products are 1 and – 6 respectively
Answer» Equation of a line in intercept form is \(\frac{x}{a}+\frac{y}{b}=1\) Given, a + b = 1 and a × b = – 6 ⇒ a −\(\frac{6}{a}\) = 1 ⇒ a² − a − 6 = 0 ⇒ (a − 3) (a + 2) = 0 ⇒ a = 3, – 2. If a = 3, b = – 2 and if a = – 2, b = 3. ∴ Equation of the line is \(\frac{x}{3}-\frac{y}{2}=1\) or \(\frac{x}{-2}-\frac{y}{3}=1\) ⇒ 2x – 3y – 6 = 0 or 3x – 2y + 6 = 0, is the required equation of the line

Find the equation of the lines which cut-off intercepts on the axes whose sum and products are 1 and – 6 respectively

Answer»

Equation of a line in intercept form is

\(\frac{x}{a}+\frac{y}{b}=1\)

Given, a + b = 1

and a × b = – 6

⇒ a −\(\frac{6}{a}\) = 1

⇒ a² − a − 6 = 0

⇒ (a − 3) (a + 2) = 0

⇒ a = 3, – 2.

If a = 3, b = – 2 and if a = – 2, b = 3.

∴ Equation of the line is

\(\frac{x}{3}-\frac{y}{2}=1\) or \(\frac{x}{-2}-\frac{y}{3}=1\)

⇒ 2x – 3y – 6 = 0 or 3x – 2y + 6 = 0,

is the required equation of the line