(A) The equation of the straight line is $ax + by + c = 0$.Since the line always passes through the point $(1, -2),$ we substitute $x = 1$ and $y = -2

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(A) The equation of the straight line is $ax + by + c = 0$.Since the line always passes through the point $(1, -2),$ we substitute $x = 1$ and $y = -2$ into the equation:$a(1) + b(-2) + c = 0$$a - 2b + c = 0$Rearranging the terms,we get:$a + c = 2b$This condition $a + c = 2b$ implies that $a, b,$ and $c$ are in Arithmetic Progression $(A.P.)$.

Class 11 Mathematics Straight Line Slope of line, Equation of line in different forms

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If the straight line $ax + by + c = 0$ always passes through $(1, -2),$ then $a, b, c$ are

A
In $A.P.$
B
In $H.P.$
C
In $G.P.$
D
None of these

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Straight Line

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Slope of line, Equation of line in different forms

The equation of a line passing through the intersection of lines $x = 0$ and $y = 0$ and through the point $(2, 2)$ is:

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The length of the segment of the straight line passing through $(3,3)$ and $(7,6)$ cut off by the coordinate axes is

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Find the equation of the line passing through $(4, 6)$ and parallel to the line $3x - 7y + 2 = 0$.

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The gradient of the line joining the points on the curve $y = x^2 + 2x$ whose abscissae are $1$ and $3$,is

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What is the equation of the line that makes an angle of $45^{\circ}$ with the $x$-axis and passes through the point $(3, -4)$?

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If the straight line $ax + by + c = 0$ always passes through $(1, -2),$ then $a, b, c$ are

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The equation of a line passing through the intersection of lines $x = 0$ and $y = 0$ and through the point $(2, 2)$ is:

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