Question

For circle \(x^2+y^2+12x-4y-9=0\), line \(x+2y-3=0\) represents

• A. tangent
• B. chord but not diameter
• C. diameter
• D. polar but not chord or tangent \bigskip

Hint:

If distance < radius → chord.

Answer 1

The Correct Option is B

Concept: Check position of line w.r.t circle using distance from center.

Step 1: Find center and radius.
\[ (x+6)^2+(y-2)^2=49 \] Center \(C(-6,2)\), radius \(7\)

Step 2: Distance from center to line.
\[ \frac{| -6+4-3 |}{\sqrt5}=\frac{5}{\sqrt5}=\sqrt5 \] \[ \sqrt5 < 7 \]

Step 3: Conclusion.
Line cuts circle ⇒ chord, not diameter. \[ \boxed{(B)} \]