Question

The area (in square unit) of the circle which touches the lines $4x+3y=15$ and $4x+3y=5$ is

• A. $4\pi$
• B. $3\pi$
• C. $2\pi$
• D. $\pi$

Hint:

For two parallel lines $ax+by+c_1=0$ and $ax+by+c_2=0$, the distance between them is $\frac{|c_1 - c_2|}{\sqrt{a^2 + b^2}}$.

Answer 1

The Correct Option is D

Step 1: Distance Between Lines
The two lines are parallel. The distance between them is the diameter of the circle.
$d = \frac{|c_1 - c_2|}{\sqrt{a^2 + b^2}} = \frac{|15 - 5|}{\sqrt{4^2 + 3^2}} = \frac{10}{5} = 2$.
Step 2: Determine Radius
Diameter $d = 2$, so radius $r = \frac{2}{2} = 1$.
Step 3: Calculate Area
Area $= \pi r^2 = \pi(1)^2 = \pi$ square unit.
Final Answer: (d)