Question

Find the equation of the line through the intersection of lines 2x —y = 1 and 2y -9 and making an angle 300 with positive direction of x- axis.​

Answer 1

EXPLANATION.

Equation of the line through the intersecting of lines,

(1) = 2x - y = 1.

(2) = 2y - 9 = 0.

Makes an angle 30° with positive x-axis.

From equation (2) we get,

⇒ 2y - 9 = 0.

⇒ 2y = 9.

⇒ y = 9/2.

Put the value of y = 9/2 in equation (1) we get.

⇒ 2x - 9/2 = 1.

⇒ 2x = 1 + 9/2.

⇒ 2x = 2 + 9/2.

⇒ 2x = 11/2.

⇒ x = 11/4.

As we know that,

Slope = m = tan∅.

⇒ m = tan(30°).

⇒ m = 1/√3.

As we know that,

Equation of line = (y - y₁) = m(x - x₁).

Put the value in the equation, we get.

⇒ (y - 9/2) = 1/√3 (x - 11/4).

⇒ √3(2y - 9/2) = (4x - 11/4).

⇒ √3(2y - 9) = (4x - 11/2).

⇒ 2√3(2y - 9) = 4x - 11.

⇒ 4√3y - 18√3 = 4x - 11.

⇒ 4x - 4√3y + 7 = 0.

Answer 2

...❀A NS WE R❀...

Equation of the line through the interesecting of the line:

☆(1) 2x —y = 1

☆(2) 2y -9 = 0

make an angle 30° with positive x axis.

from equation (2) we get,

➣2 y - 9 = 0

➣2 y = 9

➣y = 9/2

put the value of y = 9/2 in equation 1 we have get :

➢2 x - 9/2 = 1

➢2 x = 1 + 9/2

➢2 x = 2 + 9/2

➢2 x = 11/2

➢x = 11/4

➱( y - 9/2 )= 1 √(x -11 / 4)

➱√3 ( 2 y - 9/2) = 4 x - 11/4

➱√3 ( 2 y - 9 )= 4 x - 11/4

➱2√3 ( 2 y - 9 ) = 4 x - 11

➱4√3 y - 18 √3 = 4 x - 11

⇝4 x - 4√3y + 7 = 0