Joint equation of two lines through the origin such that one is parallel to line x+2y=5

Try the new Google Books

Check out the new look and enjoy easier access to your favorite features

Find the joint equation of the pair of lines through the origin , one of which is parallel to 2x+y=5 and other is perpendicular to 3x 4x+7=0.

Open in App

The combined equation of the pair of lines through origin such that one is parallel to 3x + 2y = 3 and the other is perpendicular to 6x + 3y + 17 = 0 is ______.

• 3x2 + 4xy + 4y2 = 0

• 3x2 - 4xy - 4y2 = 0

• 3x2 - 4xy + 4y2 = 0

• 3x2 - 8xy + 4y2 = 0

The combined equation of the pair of lines through origin such that one is parallel to 3x + 2y = 3 and the other is perpendicular to 6x + 3y + 17 = 0 is 3x2 - 4xy - 4y2 = 0.

Explanation:

Slope ofline 3x + 2y = 3 is `(-3)/2`

∴ Line parallel to 3x + 2y = 3 and passing through origin is y = `(-3)/2`x

⇒ 3x + 2y = 0

Slope of 6x + 3y + 17 = 0 is - 2

∴ Line perpendicular to 6x + 3y + 17 = 0 and passing through origin is y = `1/2`x

⇒ x - 2y = 0

Their combined equation is

(3x + 2y) (x - 2y) = 0

⇒ 3x2 - 6xy + 2yx - 4y2 = 0

⇒ 3x2 - 4xy - 4y2 = 0

Concept: Formation of Joint Equation and Separation of Equations from a Given Equation

  Is there an error in this question or solution?

Find the joint equation of the line passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18

Let L1 and L2 be the lines passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18 respectively.

Slopes of the lines x + 2y = 19 and 3x + y = 18 are `-1/2` and `- 3/1` = -3 respectively.

∴ slopes of the lines L1 and L2 are 2 and `1/3` respectively.

Since the lines L1 and L2 pass through the origin, their equations are

y = 2x  and y = `1/3`x

i.e. 2x - y = 0  and x - 3y = 0

∴ their combined equation is

(2x - y)(x - 3y) = 0

∴ 2x2 - 6xy - xy + 3y2 = 0

∴ 2x2 - 7xy + 3y2 = 0 

Concept: Combined Equation of a Pair Lines

  Is there an error in this question or solution?