Question

Let ${\theta }_1$ be the angle between two lines $2x+3y+C_1=0$ and $-x+5y+c_2=0$ and ${\theta }_2$ be the angle between two fines $2x+3y+cx=0$ and $-x+5y+c_3=0,$ where $c_1{c}_2,c_3$ are any real numbers:
Statement-1: If $c_2$ and $c_3$ are proportional, then ${\theta }_1={\theta }_2$.
Statement-1: ${\theta }_1=$${\theta }_2$ for all $c_2$ and $c_3$

• A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation of Statement-1
• B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation of Statement-1
• C. Statement-1 is false; Statement-2 is true
• D. Statement-1 is true; Statement-2 is false

Answer 1

Answer: (A)

Two lines $-x+5y+c_2=0$ and$-x+5y+c_3=0$ are parallel to each other. Hence statement-1 is true, statement-2 is true and statement-2 is the correct explanation of statement-1.