Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XI  >>  Math  >>  Conic Sections
0 votes

If the lines $3x – 4y + 4 = 0$ and $6x – 8y – 7 = 0$ are tangents to a circle, then find the radius of the circle

$\begin{array}{1 1}\large\frac{3}{2}\text{units}\\\large\frac{3}{4}\text{units}\\\large\frac{3}{8}\text{units}\\\large\frac{3}{5}\text{units}\end{array} $

Can you answer this question?

1 Answer

0 votes
  • If the slopes of two lines are equal,then the lines are parallel.
  • The distance between the parallel tangents gives the diameter of the circle.
  • Distance between the parallel lines is $d= \bigg|\large\frac{C_1-C_2}{\sqrt{A^2+B^2}}\bigg|$
Answer : $\large\frac{3}{4}$ units
The equation of the given tangents are $3x-4y+4 = 0$ and $6x-8y-7=0$
The slopes of the given tangents are $\large\frac{3}{4}$
Hence they are parallel tangents.
Here $C_1=4$ and $C_2 =-\large\frac{7}{2}$
$\therefore$ The diameter of the circle is $d=\bigg|\large\frac{4-(-\large\frac{7}{2})}{\sqrt{3^2+4^2}}\bigg|$
The diameter is $\large\frac{3}{2}$ units
$\therefore$ The radius is $\large\frac{3}{4}$ units.
answered Oct 8, 2014 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App