Question

The lines $3x-4y+10=0$ and $3x-4y-15=0$ are tangent to the circle, then its radius is

• A. $\frac{5}{2}$
• B. $\frac{25}{2}$
• C. $5$
• D. $25$

Answer 1

The correct option is A $\frac{5}{2}$

Equations of lines are $3x-4y+10=0$ ...(i)

and $3x-4y-15=0$ ...(ii)

We know that the given standard equation of the line is $ax+by+c=0.$

Comparing Eqs. (i) and (ii) with the standard equation, we get $a=3,b=-4,c_1=10$ and $c_2=-15.$

Since tangents are parallel to each other, therefore distance between lines (i) and (ii)

$=\frac{c_1-c_2}{\sqrt{a^2+b^2}}=\frac{10+15}{\sqrt{9+16}}=\frac{25}{5}=5$

We also know that the distance between the lines is equal to the diameter of circle.

Therefore, radius of the circle $=\frac{1}{2}$ (distance between the lines)

$=\frac{1}{2}\times 5$

$=\frac{5}{2}$