Question

The joint equation of the pair of lines through the
origin, one of which is parallel to 2x + y = 5 and the
other is perpendicular to 3x – 4y + 7 = 0 is.
(a) 8x2 - 10xy + 3y2 = 0
(b) 8x2 + 10xy + 3y2 = 0
(c) 8x + 10x7 - 3y2 = 0
(d) 8x2 - 10xy - 34- = 0​

Answer 1

Answer:B 8x2 + 10xy + 3y2 = 0

Step-by-step explanation:

3x2+5xy−6y2=0

6x2+5xy−6y2=0

x2+2xy+6y2=0

x2−5xy+y2=0

Answer 2

Concept

A pair of lines, line segments or rays are intersecting if they need a standard point. This common point is their point of intersection.

Given

The equation of pair of lines which is parallel to $2x+y=5$ and perpendicular to $3x-4y+7=0$.

Find

We have to seek out the joint equation of the pair of lines through the

Solution

Firstly, we'll find the line which is parallel to the line $2x+y=5$.

Equation of line parallel to $2x+y=5$ and spending through the origin is $2x+y=0$.

Now, we'll find the line which is perpendicular to the line $3x-4y+7=0$.

Equation of line perpendicular to $3x-4y+7=0$ and spending through the origin is $4x+3y=0$.

Further, we'll combined both equations with multiplying one aother, we get

$(2x+y)(4x+3y)=0$

Furthermore, we'll simplify the above expression, we get

$\begin{aligned}8x^2+6xy+4xy+3y^2&=0\\ 8x^2+10xy+3y^2=0\end$

Hence, option (B) is correct.

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