Question:
<p>The normal to the circle x<sup>2</sup> + y<sup>2</sup> - 3x - 6y - 10 = 0 at the point (-3, 4) is</p>
<p style="display:inline">9x - 2y + 35 = 0</p>
<p style="display:inline">2x - 9y + 30 = 0</p>
<p style="display:inline">2x + 9y - 30 = 0</p>
<p style="display:inline">2x - 9y - 30 = 0</p>
Step-by-Step Solution
Key Concept: The normal to a circle at any point is the straight line passing through both the given point and the center of the circle.
<p>The equation of normal to the circle<br />
x<sup>2</sup> + y<sup>2</sup> + 2gx + 2fy + c = 0 at (x<sub>1</sub>, y<sub>1</sub>) is<br />
<span class="math-tex">\(\frac{x-x_{1}}{x_{1}+g}=\frac{y-y_{1}}{y_{1}+f}\)</span><br />
<span class="math-tex">\(\Rightarrow \frac{x+3}{-3-\frac{3}{2}}=\frac{y-4}{4-3}\)</span><br />
<span class="math-tex">\(\Rightarrow\)</span> 2x + 9y - 30 = 0</p>
Correct Answer: C