Question

Find the equation of the hyperbola with foci at (7,0) and lengti
Find the equation of the hyperbola, the length of whose focal chord, perpendicular to the
transverse axis, is 8 units and the co-ordinates of the foci are (0, +3/5).​

Answer 1

Answer:

We have,

conjugate axis(perpendicular to transverse axis) =2b=8 units

foci = (0, ±3/5) =(0, ±y)

because the foci lies on y-axis

so, the equation of hyperbola, follow as

y²/a²-x²/b²=1

2b=8

b=8/2=4

b=4

(0, ±c) =(0, ±3/5)

c=3/5

b²=c²-a²

Or, a²=c²-b²

Or, a²=(3/5)²-(4)²

Or, a²=9/25-16

Or, a=√9/25-16

Or, a=-77/5

Hence,

y²/(5929/25)-x²/(4)²=1

=25y²/5929-x²/16=1

The Equation of Hyperbola =5y²/77-x²/16=1