(D) Let the points be $A(-a, -b)$,$B(a, b)$,and $C(a^2, ab)$.Calculate the slopes of the line segments:Slope of $AB = \frac{b - (-b)}{a - (-a)} = \fra

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(D) Let the points be $A(-a, -b)$,$B(a, b)$,and $C(a^2, ab)$.Calculate the slopes of the line segments:Slope of $AB = \frac{b - (-b)}{a - (-a)} = \frac{2b}{2a} = \frac{b}{a}$.Slope of $BC = \frac{ab - b}{a^2 - a} = \frac{b(a - 1)}{a(a - 1)} = \frac{b}{a}$.Since the slope of $AB$ is equal to the slope of $BC$ and they share a common point $B$,the points $A, B$,and $C$ are collinear.

Class 11 Mathematics Straight Lines Concurrency of three lines

Easy

The points $(-a, -b), (a, b), (a^2, ab)$ are

A
Vertices of an equilateral triangle
B
Vertices of a right angled triangle
C
Vertices of an isosceles triangle
D
Collinear

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Straight Lines

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Concurrency of three lines

The lines $x-y-2=0$,$x+y-4=0$,and $x+3y=6$ meet at a common point:

EasyTS EAMCET 2006

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Find the equation of the line passing through the point of intersection of the lines $x + y - 2 = 0$ and $2x - y + 1 = 0$ and the origin $(0, 0)$.

Easy

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The three lines $lx + my + n = 0$,$mx + ny + l = 0$,and $nx + ly + m = 0$ are concurrent if:

Easy

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Given the four lines with equations $x + 2y = 3,$ $3x + 4y = 7,$ $2x + 3y = 4,$ and $4x + 5y = 6,$ these lines are:

EasyIIT 1980

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The line parallel to the $x$-axis and passing through the intersection of the lines $ax + 2by + 3b = 0$ and $bx - 2ay - 3a = 0$,where $(a, b) \ne (0, 0)$ is

MediumAIEEE 2005

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The points $(-a, -b), (a, b), (a^2, ab)$ are

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The lines $x-y-2=0$,$x+y-4=0$,and $x+3y=6$ meet at a common point:

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