Question: A line AB makes zero intercepts on x?axis and y?axis and it is perpendicular to another line CD, $ 3x+4y+6=0. $ The equation of line AB is [Karnataka CET 2001]
Options:
A) $ y=4 $
B) $ 4x-3y+8=0 $
C) $ 4x-3y=0 $
D) $ 4x-3y+6=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, line AB making 0 intercepts on x-axis and y-axis or $ (x_1,y_1)\equiv (0,0) $ and the line is perpendicular to line $ CD,3x+4y+6=0 $ . We know that standard equation of a line is $ y=ax+b. $ Comparing given equation of line CD with the standard equation, we get $ a=3 $ and $ b=4 $ . We also know that slope of the given line $ CD=-\frac{a}{b}=\frac{-3}{4}. $ Since the line AB is perpendicular to the line CD, therefore slope of the line $ AB(m)=\frac{4}{3} $ . Thus relation for the equation of the line AB will be $ (y-y_1)=m(x-x_1) $ or $ y-0=\frac{4}{3}(x-0) $ or $ 3y=4x $ or $ 4x-3y=0 $ .
BETA
