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NCERT Class XI Mathematics - Straight Lines - Solutions

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Question : 13 of 74
Marks: +1, -0
If three points (h, 0), (a, b) and (0, k) lie on a line, show that ah+bk\frac{a}{h} + \frac{b}{k} = 1
Solution:  
Let A(h, 0), B(a, b) and C(0, k) be the given collinear points.
∴ Slope of AB = Slope of BC
⇒ b−0a−h\frac{b-0}{a-h} = k−b0−a\frac{k-b}{0-a} ⇒ ba−h\frac{b}{a-h} = b−ka\frac{b-k}{a}
⇒ ab = (a – h) (b – k) ⇒ ab = ab – ak – hb + hk ⇒ ak + hb = hk
Dividing both sides by hk, we have ah+bk\frac{a}{h} + \frac{b}{k} = 1
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