A) \[{{30}^{o}}\]and \[{{45}^{o}}\]
B) \[{{45}^{o}}\] and \[{{60}^{o}}\]
C) Equal
D) Parallel to axes
Correct Answer: C
Solution :
We get the desired lines by homogenising the equation of curve w.r.t. line. \[5{{x}^{2}}+12xy-8{{y}^{2}}+8x-4y+12=0\] or \[5{{x}^{2}}+12xy-8{{y}^{2}}+(8x-4y)\left( \frac{x-y}{2} \right)+12\text{ }{{\left( \frac{x-y}{2} \right)}^{2}}=0\] \[\Rightarrow 5{{x}^{2}}+12xy-8{{y}^{2}}+4{{x}^{2}}-4xy-2xy+2{{y}^{2}}+3{{x}^{2}}\] \[+3{{y}^{2}}-6xy=0\] \[\Rightarrow 12{{x}^{2}}-3{{y}^{2}}=0\] or \[4{{x}^{2}}-{{y}^{2}}=0\] or \[(2x-y)(2x+y)=0\]; \[\therefore {{m}_{1}}=2,\ \ \ {{m}_{2}}=-2\].
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