Pair Of Straight Lines Question 28
Question: Angle between the line joining the origin to the points of intersection of the curves $ 2x^{2}+3y^{2}+10x=0 $ and $ 3x^{2}+5y^{2}+16x=0 $ is
Options:
A) $ {{\tan }^{-1}}\frac{3}{2} $
B) $ {{\tan }^{-1}}\frac{4}{5} $
C) $ 90^{o} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
The equation of any curve through the points of intersection of the given curves is $ 2x^{2}+3y^{2}+10x+\lambda (3x^{2}+5y^{2}+16x)=0 $ …..(i)
If this equation represents two straight lines through the origin, then this must be homogeneous equation of second degree i.e., coefficient of x in (i) must vanish
$ 10+16\lambda =0\Rightarrow \lambda =\frac{-10}{16}=\frac{-5}{8} $
Substituting this value of $ \lambda $ in (i), we get the equation of pair of straight lines $ x^{2}-y^{2}=0 $ …(ii)
Hence the lines represented by the equation (ii) are mutually perpendicular.
BETA
