(D) Given equations are $y - x + 7 = 0$ $(1)$ and $y + 2x - 2 = 0$ $(2)$.Subtracting $(1)$ from $(2)$,we get $(y + 2x - 2) - (y - x + 7) = 0$,which si

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(D) Given equations are $y - x + 7 = 0$ $(1)$ and $y + 2x - 2 = 0$ $(2)$.Subtracting $(1)$ from $(2)$,we get $(y + 2x - 2) - (y - x + 7) = 0$,which simplifies to $3x - 9 = 0$,so $x = 3$.Substituting $x = 3$ in $(1)$,we get $y - 3 + 7 = 0$,so $y = -4$.The point of intersection is $(3, -4)$.The equation of a line passing through the origin $(0, 0)$ and $(x_1, y_1)$ is given by $y = \frac{y_1}{x_1}x$.Substituting $(3, -4)$,we get $y = \frac{-4}{3}x$,which implies $3y = -4x$ or $4x + 3y = 0$.

Class 11 Mathematics Pair of straight lines Equation of lines joining the origin to the point of intersection of a curve and a line and Distance between the pair of lines

Easy

The equation of the straight line joining the origin to the point of intersection of $y - x + 7 = 0$ and $y + 2x - 2 = 0$ is

A
$3x + 4y = 0$
B
$3x - 4y = 0$
C
$4x - 3y = 0$
D
$4x + 3y = 0$

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Pair of straight lines

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Equation of lines joining the origin to the point of intersection of a curve and a line and Distance between the pair of lines

The equation $8x^2 + 8xy + 2y^2 + 26x + 13y + 15 = 0$ represents a pair of parallel straight lines. The distance between them is

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If $\theta$ is the acute angle between the lines joining the origin to the points of intersection of the curve $x^2+xy+y^2+x+3y+1=0$ and the straight line $x+y+2=0$,then $\cos \theta=$

EasyTS EAMCET 2023

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The angle between the lines joining the origin to the points of intersection of the line $y = 3x + 2$ and the curve $x^{2} + 2xy + 3y^{2} + 4x + 8y - 11 = 0$ is:

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The lines joining the points of intersection of the line $x + y = 1$ and the curve $x^2 + y^2 - 2y + \lambda = 0$ to the origin are perpendicular. Then the value of $\lambda$ is:

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If the lines joining the origin to the points of intersection of $y=mx+1$ and $x^2+y^2=1$ are perpendicular,then .........

MediumAP EAMCET 2020

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The equation of the straight line joining the origin to the point of intersection of $y - x + 7 = 0$ and $y + 2x - 2 = 0$ is

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