Coordinate Geometry
Line between two circles without cutting a chord
Grade Class 12
Question:
The number of integral values of $k$ for which the line $3x+4y-k=0$ lies between the circles $x^2+y^2-2x-2y+1=0$ and $x^2+y^2-18x-12y+113=0$, without cutting a chord on either circle, is equal to
Step-by-Step Solution
Key Concept: A line lies between two circles without cutting either if the distance from each circle's center to the line is greater than the respective radius, and the line separates the two circles.
$k\in[12,41]$: 30 integral values.
Correct Answer: 30