First slide

Equation of line in Straight lines

Question

If a, c, b are three terms of a G.P., then the line ax + by + c = 0

Moderate

A

has a fixed direction
B

always passes through a fixed point
C

forms a triangle with the axes whose area is constant
D

always cuts intercepts on the axes such that their sum is zero.

Solution

Since a, c, b are in G.P.,
$∴ c^{2} = a b$ (1)
The area of the triangle
$= \frac{1}{2} \times (- \frac{c}{a}) \times (- \frac{c}{b})$
$= \frac{1}{2} \times \frac{c^{2}}{a b} = \frac{1}{2}$ [Using (1)]
= constant

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