Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola $\dfrac{y^2}{25} - \dfrac{x^2}{9} = 1$.

Here $A^2=25$ (under $y^2$), $B^2=9$ (under $x^2$), so $A=5,\,B=3$; the transverse axis is the $Y$-axis. $e^2=1+\dfrac{B^2}{A^2}=1+\dfrac{9}{25}=\dfrac{34}{25} \Rightarrow e=\dfrac{\sqrt{34}}{5}$. - Transverse axis $=2A=10$; conjugate axis $=2B=6$. - Foci $(0,\pm Ae)=(0,\pm\sqrt{34})$. - Directrices $y=\pm\dfrac{A}{e}=\pm\dfrac{25}{\sqrt{34}}=\pm\dfrac{25\sqrt{34}}{34}$. …

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equa

Exercise 7.3 · Q70

\dfrac{y^2}{25} - \dfrac{x^2}{9} = 1

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Here $A^2=25$ (under $y^2$ ), $B^2=9$ (under $x^2$ ), so $A=5,\,B=3$ ; the transverse axis is the $Y$ -axis.

$e^2=1+\dfrac{B^2}{A^2}=1+\dfrac{9}{25}=\dfrac{34}{25} \Rightarrow e=\dfrac{\sqrt{34}}{5}$ .

Transverse axis $=2A=10$ ; conjugate axis $=2B=6$ .
Foci $(0,\pm Ae)=(0,\pm\sqrt{34})$ .
Directrices $y=\pm\dfrac{A}{e}=\pm\dfrac{25}{\sqrt{34}}=\pm\dfrac{25\sqrt{34}}{34}$ . …

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Q.Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola $\dfrac{y^2}{25} - \dfrac{x^2}{9} = 1$ .

Concept understanding — Focal Properties and Latus Rectum of a Hyperbola

Q.Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola y225−x29=1\dfrac{y^2}{25} - \dfrac{x^2}{9} = 125y2​−9x2​=1.

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Q.Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola $\dfrac{y^2}{25} - \dfrac{x^2}{9} = 1$ .

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