If the normal at angle ϕ on the hyperbola x2a2−y2b2=1 meets the transverse axis at G such that AG⋅A′G=am(ensecpϕ−1), where A,A′ are the vertices of the hyperbola, e is the eccentricity and m,n and p are positive integers, then value of (m+n+p) is

If the normal at angle ϕ on the hyperbola x2a2−y2b2=1 meets the tra

1.	If the normal at angle ϕ on the hyperbola x2a2−y2b2=1 meets the transverse axis at G such that AG⋅A′G=am(ensecpϕ−1), where A,A′ are the vertices of the hyperbola, e is the eccentricity and m,n and p are positive integers, then value of (m+n+p) is
Answer» If the normal at angle $ϕ$ on the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ meets the transverse axis at $G$ such that $A G \cdot A^{'} G = a^{m} (e^{n} {sec}^{p} ϕ - 1)$ , where $A, A^{'}$ are the vertices of the hyperbola, $e$ is the eccentricity and $m, n$ and $p$ are positive integers, then value of $(m + n + p)$ is