Question:
The slope of the common tangent drawn to the circles
$$
x^2 + y^2 - 4x + 12y - 216 = 0
$$
and
$$
x^2 + y^2 + 6x - 12y + 36 = 0
$$
is:
The slope of the common tangent drawn to the circles
$$
x^2 + y^2 - 4x + 12y - 216 = 0
$$
and
$$
x^2 + y^2 + 6x - 12y + 36 = 0
$$
is:
Show Hint
Use geometry of circles and tangent line formulas to find slope.
Updated On: Jun 4, 2025
- 1
- -1
- $\frac{5}{12}$
- $\frac{12}{7}$
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The Correct Option is C
Solution and Explanation
Calculate centers and radii of circles. Use formula for slope \( m \) of common tangent to two circles: \[ m = \frac{r_1 \pm r_2}{d} \] After calculations, slope is \( \frac{5}{12} \).
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