Question

$\tt{If \: three \: points \: (h , 0),(a , b),(0 , k) \: lie \: \: on \: a}$
$\tt{ line, show \: that:-}$

$\huge\bold{\tt\red{\frac{a}{h} + \frac{b}{k} = 1}}$
​

Answer 1

If the points A(h,0),B(a,b) and C(0,k) lie on line,

then,

Slope of AB=slope of BC

b-0 k-b

a-h =. 0-a

b k-b

a-h = -a

⇒−ab=(k−b)(a−h)

⇒−ab=ka−kh−ab+bh

⇒ka+bh=kh

On dividing both sides by kh, we obtain

ka + bh. kh

kh. kh = kh

a. + b = 1

h. k

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