Question

If \( Q(h, k) \) is the inverse point of \( P(1,2) \) with respect to the circle \( x^2 + y^2 - 4x + 1 = 0 \), then \( 2h + k \) is:

• A. \( 3 \)
• B. \( 4 \)
• C. \( 7 \)
• D. \( 11 \)

Hint:

The inverse point of a point \( P(x_1, y_1) \) with respect to a circle is given by: \[ Q \left( \frac{r^2 x_1}{(x_1 - a)^2 + (y_1 - b)^2}, \frac{r^2 y_1}{(x_1 - a)^2 + (y_1 - b)^2} \right) \]

Answer 1

The Correct Option is B

The inverse point formula with respect to a circle is: \[ h = \frac{r^2 x_1}{(x_1 - a)^2 + (y_1 - b)^2}, \quad k = \frac{r^2 y_1}{(x_1 - a)^2 + (y_1 - b)^2} \] After solving, we obtain: \[ 2h + k = 4 \]