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प्रश्न
If the intercept of a line between the coordinate axes is divided by the point (–5, 4) in the ratio 1 : 2, then find the equation of the line.
उत्तर
Let a and b be the intercepts on the given line.
∴ Coordinates of A and B are (a, 0) and (0, b) respectively
∴ – 5 = `(1 xx 0 + 2 xx a)/(1 + 2)`
⇒ 2a = – 15 .......`[(because "X" = (m_1x_2 + m_2x_1)/(m_1 + m_2)),("and" "Y" = (m_1y_2 + m_2y_1)/(m_1 + m_2))]`
⇒ a = ` (-15)/2`
∴ A = `((-15)/2, 0)`
And 4 = `(1 xx b + 0 xx 2)/(1 + 2)`
⇒ 4 = `b/3`
⇒ b = 12
∴ B = (0, 12)
So, the equation of line AB is
y – y1 = `(y_2 - y_1)/(x_2 - x_1) (x - x_1)`
y – 0 = `((12 - 0)/(0 + 15/2)) (x + 15/2)`
⇒ y = `(12 xx 2)/15 (x + 15/2)`
⇒ y = `8/5(x + 15/2)`
⇒ 5y = 8x + 60
⇒ 8x – 5y + 60 = 0
Hence, the required equation is 8x – 5y + 60 = 0.
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