Equation of line in Straight lines

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Suppose that a,b,c are in arithmetic progression then the line $ax + by + c = 0$ passes through the fixed point $(l, m)$ then $l + m =$

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Solution

Given a,b,c are in arithmetic progression, so that $b = \frac{a + c}{2}$
Substitute $b = \frac{a + c}{2}$ in the equation $ax + by + c = 0$
$\begin{matrix} ax + (\frac{a + c}{2}) y + c = 0 \\ 2 ax + (a + c) y + 2 c = 0 \\ a (2 x + y) + c (y + 2) = 0 \end{matrix}$
This represents the set of all lines passing through the point of intersection of $2 x + y = 0$ and $y + 2 = 0$
The point of intersection is $(1, - 2)$
Hence $l + m = 1 - 2 = - 1$

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Equation of line in Straight lines

Remember concepts with our Masterclasses.

Suppose that a,b,c are in arithmetic progression then the line ax+by+c=0 passes through the fixed point l,m then l+m=

Given a,b,c are in arithmetic progression, so that b=a+c2Substitute b=a+c2 in the equation ax+by+c=0ax+a+c2y+c=02ax+a+cy+2c=0a2x+y+cy+2=0 This represents the set of all lines passing through the point of intersection of 2x+y=0 and y+2=0The point of intersection is 1,−2Hence l+m=1−2=−1

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Suppose that a,b,c are in arithmetic progression then the line $ax + by + c = 0$ passes through the fixed point $(l, m)$ then $l + m =$