Comprehension (Q. 5 & 6) Let `A B` be any chord of the circle `x^2+y^2-2x-6y-6=0` which subtends a right angle at the point (2, 4). Locus of mid point of `A B` is (A) `x^2+y^2-7y-16=0` (B)`x^2+y^2-3x-7y+7=0` (C)`x^2+y^2+3x+7y-16=0` (D)`x^2+y^2+3x+7y-7=0`

Explanation

To find the locus of the midpoint of the chord \( AB \) of the circle given by the equation \( x^2 + y^2 - 2x - 6y - 6 = 0 \) that subtends a right angle at the point \( (2, 4) \), we can follow these steps:

### Step 1: Rewrite the Circle Equation
First, we need to rewrite the equation of the circle in standard form. The given equation is:

\[ x^2 + y^2 - 2x - 6y - 6 = 0 \]
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