A) 0
B) 1
C) 2
D) 3
Correct Answer: B
Solution :
[b] The given points are\[A(h,0),B(a,b),C(0,k)\], they lie on the same plane. \[\therefore \,\,\,\,\,\,\,Slope\,\,of\,\,AB=Slope\,\,of\,\,BC\] \[\therefore \] Slope of \[AB=\frac{b-0}{a-h}=\frac{b}{a-h};\] Slope of \[BC=\frac{k-b}{0-a}=\frac{k-b}{-a}\] \[\therefore \frac{b}{a-h}=\frac{k-b}{-a}\] or by cross multiplication \[-ab=(a-h)(k-b)\] or \[-ab=ak-ab-hk+hb\] or \[0=ak-hk+hb\] or \[ak+hb=hk\] Dividing by \[hk\Rightarrow \frac{ak}{hk}+\frac{hb}{hk}=1\] or \[\frac{a}{h}+\frac{b}{k}=1\]
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