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

If `H(x,y)=0` represents the equation of a hyperbola and `A(x,y)=0`, `

1.	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 inA. `A.P.`B. `G.P.`C. `H.P.`D. none of these
Answer» Let `H(x,y)=(x^(2))/(a^(2))-(y^(2))/(b^(2))-1`. Then, `A(x,y)=(x^(2))/(a^(2))-(y^(2))/(b^(2))` and `C(x,y)=(x^(2))/(a^(2))-(y^(2))/(b^(2))+1` We observe that `2A(alpha,beta)=H(alpha,beta)+C(alpha,beta)` Hence, `H(alpha,beta)`, `A(alpha,beta)` and `C(alpha,beta)` are in `A.P`.

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