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प्रश्न
Point R (h, k) divides a line segment between the axes in the ratio 1 : 2. Find the equation of the line.
उत्तर
The equation of the line with intercepts a and b is \[\frac{x}{a} + \frac{y}{b} = 1\].
The line passes through R (h, k).
∴ \[\frac{h}{a} + \frac{k}{b} = 1\] ... (1)
The line intersects the coordinate axes at A (a, 0) and B (0, b).
Here, AP : PB = 1 : 2
\[\therefore h = \frac{1 \times 0 + 2 \times a}{1 + 2}, k = \frac{1 \times b + 2 \times 0}{1 + 2}\]
\[ \Rightarrow a = \frac{3h}{2}, b = 3k\]
Substituting
\[a = \frac{3h}{2}, b = 3k\] in \[\frac{x}{a} + \frac{y}{b} = 1\]
\[\frac{2x}{3h} + \frac{y}{3k} = 1\]
\[ \Rightarrow 2kx + hy - 3hk = 0\]
Hence, the equation of the line is \[2kx + hy - 3hk = 0\]
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