If an equation hxy+gx+fy+c=0 represents a pair of lines, then

MHT CET 2024 Mathematics question

If an equation represents a pair of lines, then

(A)fg = chCorrect
(B)gh = cf
(C)fh = cg
(D)hf = -cg

Answer: (A)

Solution

Write hxy+gx+fy+c=\frac1h\left[(hx+f)(hy+g)\right]+c-\frac{fg}{h} since (hx+f)(hy+g)=h^2xy+ghx+fhy+fg. So the equation is . It splits into two straight lines exactly when the constant term vanishes: ch-fg=0\Rightarrow fg=ch.

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Question ID VK-095097