AP EAMCET2002MathematicsCircle
The line y=m x+c intercepts the circle x^2+y^2=r^2 in two distinct points, if
Options
- A-r 1+m^2 < c < r 1+m^2
- Bc < -r 1+m^2
- Cc < r 1+m^2
- DNone of the above
Correct answer
A. -r 1+m^2 < c < r 1+m^2
Step-by-step solution
Equation of the circle is x^2+y^2=r^2 and the line is m x-y+c=0 The line (ii) intersect (i) in two distinct points, if the length of the ^r from the centre (0,0) to the line (ii) is less then r Thus, | 0-0+c m^2+1 | < r array ccc & |c| < r m^2+1 & -r m^2+1 < c < r m^2+1 array