Question

If a circle whose centre is (1,-3) touches the line 3x-4y-5=0 find the radius of the circle

Answer 1

Radius of circle is 2.

Step-by-step explanation:

1. Tangent on circle is always perpendicular to radius of circle.

2. We know that perpendicular distance from point  $\mathbf{(x_{1},y_{1})}$ to line Ax+By+C=0

  $\mathbf{D=\frac{Ax_{1}+By_{1}+C}{\sqrt{A^{2}+B^{2}}}}$          ...1)

3. From here equation 1)

   D= Radius of circle

   Equation of line  3x-4y-5=0

  and point is (1,-3)

  $\mathbf{R=\frac{3\times 1-4\times (-3)-5}{\sqrt{3^{2}+(-4)^{2}}}=\frac{3+12-5}{5}=\frac{10}{5}=2}$