A) 5/2
B) 5
C) 2
D) 2/5
Correct Answer: A
Solution :
Key Idea: The equation \[a{{x}^{2}}+b{{y}^{2}}+2hxy+2gx+2fy+c=0\] will represent a pair of straight lines, if \[abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}=0\]. Given equation \[{{x}^{2}}+pxy+{{y}^{2}}-5x-7y+6=0\] will represent a pair of straight lines, if \[1.1.6+2\left( -\frac{7}{2} \right)\left( \frac{-5}{2} \right)\left( \frac{p}{2} \right)-1{{\left( \frac{-7}{2} \right)}^{2}}\] \[-1{{\left( \frac{-5}{2} \right)}^{2}}-6{{\left( \frac{p}{2} \right)}^{2}}=0\] \[\Rightarrow \] \[6+\frac{35p}{4}-\frac{49}{4}-\frac{25}{4}-\frac{6{{p}^{2}}}{4}=0\] \[\Rightarrow \] \[24+35p-74-6{{p}^{2}}=0\] \[\Rightarrow \] \[6{{p}^{2}}-20p-15p+50=0\] \[\Rightarrow \] \[(2p-5)(3p-10)=0\] \[\Rightarrow \] \[p=\frac{5}{2},\frac{10}{3}\]
You need to login to perform this action.
You will be redirected in
3 sec
