Pair Of Straight Lines Question 130
Question: The angle between the lines joining the points of intersection of line $ y=3x+2 $ and the curve $ x^{2}+2xy+3y^{2}+4x+8y-11=0 $ to the origin, is
Options:
A) $ {{\tan }^{-1}}( \frac{3}{2\sqrt{2}} ) $
B) $ {{\tan }^{-1}}( \frac{2}{2\sqrt{2}} ) $
C) $ {{\tan }^{-1}}( \sqrt{3} ) $
D) $ {{\tan }^{-1}}( \frac{2}{2\sqrt{2}} ) $
Show Answer
Answer:
Correct Answer: B
Solution:
Finding the equation of lines represented by the points of intersection of curve and line with origin, we get $ x^{2}+2xy+3y^{2}+(4x+8y)( \frac{y-3x}{2} )-11\left( \frac{y-3x}{2} \right)^{2}=0 $
$ \Rightarrow x^{2}+2xy+3y^{2}+(2xy-6x^{2}+4y^{2}-12xy) $
$ -\frac{11}{4}y^{2}-\frac{99}{4}x^{2}+\frac{33}{2}xy=0 $
Proceed and find the angle between the lines represented by it using $ \alpha ={{\tan }^{-1}}\frac{2\sqrt{h^{2}-ab}}{a+b} $ .
BETA
