Find the length of the transverse axis, length of conjugate axis, the eccentricity, the coordinates of foci: x^2/ 100- y^2/25 = 1

Question

Find the length of the transverse axis, length of conjugate axis, the eccentricity, the coordinates of foci, equations of directrices, and the length of the latus rectum of the 
\(\frac {x^2}{100} - \frac {y^2}{25} = 1\)

x²/ 100- y²/25 = 1 

Answer 1

  Given equation of the hyperbola is \(\frac {x^2}{100} - \frac {y^2}{25} = 1\)

 Comparing this equation with \(\frac{x^2}{a^2} - \frac {y^2}{b^2} = 1\)

we get

a² = 100 and b² = 25

⇒ a = 10 and b = 5

Length of transverse axis = 2a = 2(10) = 20 

Length of conjugate axis = 2b = 2(5) = 10

We know that