Pair Of Straight Lines Question 71
Question: The equations to a pair of opposite sides of a parallelogram are $ x^{2}-5x+6=0 $ and $ y^{2}-6y+5=0 $ . The equations to its diagonals are
[IIT 1994; Pb. CET 2003]
Options:
A) $ x+4y=13 $ and $ y=4x-7 $
B) $ 4x+y=13 $ and $ 4y=x-7 $
C) $ 4x+y=13 $ and $ y=4x-7 $
D) $ y-4x=13 $ and $ y+4x=7 $
Show Answer
Answer:
Correct Answer: C
Solution:
Equation of diagonal $ d_1 $ is $ y-1=\frac{5-1}{3-2}(x-2) $
$ \Rightarrow y-1=\frac{4}{1}(x-2) $
$ \Rightarrow y=4x-7 $ Equation of diagonal $ d_2 $ is $ y-1=\frac{5-1}{2-3}(x-3) $
$ \Rightarrow y-1=-4(x-3)\Rightarrow 4x+y=13 $
So equations are, $ 4x+y=13 $ and $ y=4x-7 $ .
BETA
