Question

7
Find the eqution of the Straight line passing
through (-3, 10) and sum of their
Intercept
is 8.​

Answer 1

EXPLANATION.

Equation of straight lines passing through points = (-3,10).

Sum of the intercept = 8.

As we know that,

Intercept form = x/a + y/b = 1.

Let we assume that,

Sum of the intercept = a + b = 8.

⇒ b = 8 - a.

Put the value of b = 8 - a in equation, we get.

⇒ -3/a + 10/8 - a = 1.

⇒ -3(8 - a) + 10a/(a)(8 - a) = 1.

⇒ -24 + 3a + 10a = a(8 - a).

⇒ -24 + 13a = 8a - a².

⇒ -24 + 13a - 8a + a² = 0.

⇒ a² + 5a - 24 = 0.

Factorizes the equation into middle term splits, we get.

⇒ a² + 8a - 3a - 24 = 0.

⇒ a(a + 8) - 3(a + 8) = 0.

⇒ (a - 3)(a + 8) = 0.

⇒ a = 3  and  a = -8.

Put the value in equation, we get.

⇒ b = 8 - a.

⇒ b = 8 - 3.

⇒ b = 5.

⇒ b = 8 - a.

⇒ b = 8 - (-8).

⇒ b = 16.

Equation of straight lines,

⇒ a = 3  and  b = 5.

⇒ x/3 + y/5 = 1.

⇒ 5x + 3y = 15.

Equation of straight lines,

⇒ a = -8  and  b = 16.

⇒ x/-8 + y/16 = 1.

⇒ -2x + y = 16.

                                                                                                                         

MORE INFORMATION.

Equation of straight lines parallel to the axes.

(1) = Equation of x-axes ⇒ y = 0.

(2) = Equation of a line parallel to x-axes at a distance of b ⇒ y = b.

(3) = Equation of y-axes ⇒ x = 0.

(40 = Equation of a line parallel to y-axes and at a distance of a ⇒ x = a.

Answer 2

Answer:

AnswEr :

Let the Intercept be 'a' and 'b'.

• Points = ( x,y ) = ( -3,10 )
• Sum of Intercept = (a + b) = 8

» a + b = 8

» b = 8 - a

• Now A.T.Q. Point Intercept Form

$\Rightarrow \bf{ \dfrac{x}{a} + \dfrac{y}{b} = 1 }$

$\Rightarrow \bf{ \dfrac{ - 3}{a} + \dfrac{10}{(8 - a)} = 1}$

$\Rightarrow \bf{ \dfrac{ - 3(8 - a) + 10a}{a(8 - a)} = 1 }$

$\Rightarrow \bf{ \dfrac{ -24 + 3a + 10a}{8a - {a}^{2} } = 1 }$

• By Cross Multiplication

⇒ - 24 + 3a + 10a = 8a - a²

⇒ 13a - 24 = 8a - a²

⇒ a² + 13a - 8a - 24 = 0

⇒ a² + 5a - 24 = 0

• Splitting Middle Term

⇒ a² + 8a - 3a - 24 = 0

⇒ a(a + 8) - 3(a + 8) = 0

⇒ (a - 3)(a + 8) = 0

⇒ a = 3 ⠀or, ⠀a = - 8

⇒ b = (8 - 3) = 5 ⠀or, ⠀b = {8 + (- 8)} = 16

• Equation Can Be :

⋆$\large\boxed{\bf{ \dfrac{x}{3} + \dfrac{y}{5} = 1 }}$

⋆$\large\boxed{\bf{ \dfrac{x}{-8} + \dfrac{y}{16} = 1 }}$