The circle with major axis as diameter is called the auxiliary circle of the hyperbola. If a>b, then the equation of auxiliary circle is
A
x2+y2=a2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
x2+y2=b2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x2+y2=a2−b2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
x2+y2=a2+b2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Bx2+y2=a2 For any Hyperbola of the form x2a2−y2b2=1
Length of Major axis is always 2a, though a can be greater, lesser or equal to b
For any conjugate Hyperbola x2a2−y2b2=−1 or y2b2−x2a2=1
The length of major axis is always 2b, Though b can be greater, lesser or equal to a
So For any Hyperbola the circle drawn taken major axis as a diameter also called auxiliary circle of the Hyperbola will have a diameter of 2a, equal to the length of major axis and center same as center of Hyperbola.
Hence equation of Auxiliary circle of any Hyperbola will be x2+y2=a2