Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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If A, B, C Are in A.P., Then the Line Ax + by + C = 0 Passes Through a Fixed Point. Write the Coordinates of that Point. - Mathematics

Answer in Brief

If a, b, c are in A.P., then the line ax + by + c = 0 passes through a fixed point. Write the coordinates of that point.

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If, a, b, c are in A.P, then
a + c = 2b
⇒ a − 2b + c = 0
Comparing the coefficient of  ax + by + c = 0 and a − 2b + c = 0, we get
x = 1 and y = −2
So, the the coordinates of that point is (1, −2)

Concept: Straight Lines - Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
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RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Q 16 | Page 132
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