If `H(x,y)=0` represents the equation of a hyperbola and `A(x,y)=0`, `C(x,y)=0` the joint equation of its asymptotes and the conjugate hyperbola respectively, then for any point `(alpha, beta)` in the plane `H(alpha,beta)`, `A(alpha,beta)` , and `C(alpha,beta)` are in

Options

A. `A.P.`
B. `G.P.`
C. `H.P.`
D. none of these

Explanation

To solve the problem, we need to analyze the relationships between the equations of the hyperbola \( H(x, y) = 0 \), its asymptotes \( A(x, y) = 0 \), and the conjugate hyperbola \( C(x, y) = 0 \).

### Step-by-Step Solution:

1. **Identify the Equation of the Hyperbola**:
The standard form of a hyperbola is given by:
\[
\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
...