Question

If P is a point on the hyperbola 16x² – 9y² = 144 having foci at S and S , then S'P – SP = ___________________.

Answer 1

For a given hyperbola,
Let P(x, y) be any point on hyperbola,

$$\begin{gathered} 16x^{\mathit{2}}\mathit{-}9y^{\mathit{2}}=144 \\ \mathrm{i}.\mathrm{e}\mathit{.}\mathit{}\frac{x^{\mathit{2}}}{9}\mathit{-}\frac{y^{\mathit{2}}}{16}=1\mathit{}\mathrm{i}.\mathrm{e}\mathit{.}\mathit{}a=3\mathrm{and}\mathit{}b=4 \\ \mathrm{Let}\mathit{}S\mathit{}\mathrm{and}\mathit{}{S}^{\mathit{1}}\mathit{}\mathrm{represent}\mathrm{foci}\mathrm{then}\left|SP\mathit{-}S{P}^1\right|=2a \\ \mathrm{i}.\mathrm{e}.SP\mathit{-}S{P}^{\mathit{1}}=6 \end{gathered}$$