If the lines represented by $a x^{2} + 2 h x y + b y^{2} = 0$ are $u = a_{1} x + b_{1} y = 0$ and $v = a_{2} x + b_{2} y = 0$ and are coinciding then:
(a) $\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}}$
(b) $\frac{a_{1}}{b_{1}} \neq \frac{a_{2}}{b_{2}}$
(c) $a_{1} a_{1} = b_{1} b_{1}$
(d) $a_{1} a_{1} + b_{1} b_{1} = 0$

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Solution

Since lines coincides, So
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}$
or $\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}}$

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If the lines represented by ax2+2hxy+by2=0 are u=a1x+b1y=0 and v=a2x+b2y=0 and are coinciding then:(a) a1b1=a2b2(b) a1b1≠a2b2(c) a1a1=b1b1(d) a1a1+b1b1=0

Since lines coincides, Soa1a2=b1b2or a1b1=a2b2

Since lines coincides, So
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}$
or $\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}}$