The range of k for which |√x2+y2−√x2+y2−6x−8y+25|=k will represent hyperbola is
A
0<k<1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
0<k<5
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
k>5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
k>1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B0<k<5 |√(x−0)2+(y−0)2−√(x−3)2+(y−4)2|=k Comparing it with |SP−S′P|=2a S(0,0)&S′(3,4),k=2aSS′=2ae=5⇒ke=5⇒k=5e For hyperbola, e>1 ⇒0<1e<1⇒0<5e<5⇒0<k<5