A) \[\Delta =0\] and \[{{h}^{2}}=ab\]
B) \[\Delta =0\] and \[a+b=0\]
C) \[\Delta =0\] and \[{{h}^{2}}=ab\], \[{{g}^{2}}=ac\], \[{{f}^{2}}=bc\]
D) \[{{h}^{2}}=ab\], \[{{g}^{2}}=ac\] and \[{{f}^{2}}=bc\]
Correct Answer: B , C
Solution :
Comparing the given equation with the standard equation, we get \[a=4\] and\[b=-7\]. Let \[{{m}_{1}}\] and \[{{m}_{2}}\] are the slopes of given lines. Therefore sum of the slopes \[({{m}_{1}}+{{m}_{2}})=-\frac{2h}{b}=\frac{2h}{7}\] and product of the slopes\[({{m}_{1}}{{m}_{2}})=\frac{a}{b}=\frac{4}{-7}\]. \[\because {{m}_{1}}+{{m}_{2}}={{m}_{1}}{{m}_{2}}\], therefore \[\frac{2h}{7}=\frac{4}{-7}\] or \[h=-2\].Solution :
It is obvious.
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