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Byju's Answer

Standard XII

Mathematics

Equation of Planes Parallel to Axes

Find the join...

Question

Find the joint equation of the line.
$x + y - 3 = 0$ and $2 x + y - 1 = 0$ .

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Solution

$x + y = 3, 2 x + y = 1 J o i n t e q u a t i o n \Rightarrow (x + y - 3) (2 x + y - 1) = 0 \Rightarrow 2 x^{2} + x y - x + 2 x y + y^{2} - y - 6 x - 3 y + 3 = 0 \Rightarrow 2 x^{2} + y^{2} + 3 x y - 7 x - 4 y = 0 T h i s e q u a t i o n i s p a i r o f s t r a i g h t l i n e$

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Similar questions

Q. Find the joint equation of the following pair of lines :

2 x + y = 0 and 3 x - 5 y = 0

Q. Find the equation of the line joining the points of intersection of

2 x + y = 4

with

x - y + 1 = 0

and

2 x - y - 1 = 0

with

x + y - 8 = 0

Find the equation of circle which touches $2 x - y + 3 = 0$ and pass through the points of intersection of the line $x + 2 y - 1 = 0$ and the circle $x^{2} + y^{2} - 2 x + 1 = 0$

Q. Assertion (A): The joint equation of lines

y = x

and

y = - x

y^{2} = - x^{2}

i.e.

x^{2} + y^{2} = 0.

Reason (R):The joint equation of lines

a x + b y = 0

and

c x + d y = 0.

(a x + b y) (c x + d y) = 0

where

a, b, c, d

are constants.

Q. Find the equations of circles which touches

2 x - y + 3 = 0

and pass through the points of intersection of the line

x + 2 y - 1 = 0

and the circle

x^{2} + y^{2} - 2 x + 1 = 0

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Find the joint equation of the line.x+y−3=0 and 2x+y−1=0.

x+y=3,2x+y=1Jointequation⇒(x+y−3)(2x+y−1)=0⇒2x2+xy−x+2xy+y2−y−6x−3y+3=0⇒2x2+y2+3xy−7x−4y=0Thisequationispairofstraightline

Find the joint equation of the line.
$x + y - 3 = 0$ and $2 x + y - 1 = 0$ .

$x + y = 3, 2 x + y = 1 J o i n t e q u a t i o n \Rightarrow (x + y - 3) (2 x + y - 1) = 0 \Rightarrow 2 x^{2} + x y - x + 2 x y + y^{2} - y - 6 x - 3 y + 3 = 0 \Rightarrow 2 x^{2} + y^{2} + 3 x y - 7 x - 4 y = 0 T h i s e q u a t i o n i s p a i r o f s t r a i g h t l i n e$