QJEEM16Ma799e: JEE Main 2016 Mathematics - Class 11 JEEM16Ma799e Solution: A straight line through origin O meets the lines 3y = 10 − 4x…

The lines 4x + 3y $$-$$ 10 = 0 and

8x + 6y + 5 = 0 , are parallel as

    $$\frac{4}{8}$$  =  $$\frac{3}{6}$$

Now length of perpendicular from

(0, 0, 0) to 4x + 3y $$-$$ 10 = 0 is,

P₁   =   $$\left|\frac{4\left(0\right)+3\left(0\right)-10}{\sqrt{4^2+3^2}}\right|$$  =  $$\frac{10}{5}$$  =  2

Length of perpendicular from

0 (0, 0) to 8x + 6y + 5 = 0 is

P₂   =  $$\left|\frac{8\left(0\right)+6\left(0\right)+5}{\sqrt{6^2+8^2}}\right|$$   =  $$\frac{5}{10}$$   =  $$\frac{1}{2}$$

$$\therefore$$ P₁ : P₂   =   2 : $$\frac{1}{2}$$   =   4 : 1