Diameter of The Hyperbola
Category : JEE Main & Advanced
The locus of the middle points of a system of parallel chords of a hyperbola is called a diameter and the point where the diameter intersects the hyperbola is called the vertex of the diameter.
Let \[y=mx+c\] a system of parallel chords to \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] for different chords then the equation of diameter of the hyperbola is \[y=\frac{{{b}^{2}}x}{{{a}^{2}}m},\] which is passing through (0, 0).
Conjugate diameter : Two diameters are said to be conjugate when each bisects all chords parallel to the others.
If \[y={{m}_{1}}x,\,\,y={{m}_{2}}x\] be conjugate diameters, then \[{{m}_{1}}{{m}_{2}}=\frac{{{b}^{2}}}{{{a}^{2}}}\].
You need to login to perform this action.
You will be redirected in
3 sec
