A) 3
B) 9
C) 10
D) 100
Correct Answer: C
Solution :
The equation \[{{x}^{2}}-3xy+\lambda {{y}^{2}}+3x-5y+2=0\] represents a pair of straight lines. \[\therefore 2\lambda +2\left( -\frac{5}{2} \right)\text{ }\left( \frac{3}{2} \right)\text{ }\left( -\frac{3}{2} \right)-\frac{25}{4}-\frac{9\lambda }{4}-\frac{18}{4}=0\]\[\Rightarrow \lambda =2\] If \[\theta \]is the angle between the lines, then \[\tan \theta =\frac{2\sqrt{{{h}^{2}}-ab}}{a+b}=\frac{2\sqrt{(9/4)-2}}{1+2}=\frac{1}{3}\] \[\Rightarrow \text{cose}{{\text{c}}^{2}}\theta =1+{{\cot }^{2}}\theta =1+9=10\].
You need to login to perform this action.
You will be redirected in
3 sec
