Write the equation of the hyperbola of eccentricity, if it is known that the distance between its foci is 16.
Given: Distance between foci is 16 and eccentricity is
To find: equation of the hyperbola
Formula used:
Standard form of the equation of hyperbola is,
Distance between foci is given by 2ae
According to question:
2ae = 16
⇒ a2 = 32
We know,
b2 = a2(e2 – 1)
⇒ b2 = 32
Hence, equation of hyperbola is:
⇒ x2 – y2 = 32