wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The foci of the hyperbola are S(5,6),S(3,2). If its eccentricity is 2, then the equation of its directrix corresponding to focus S is

A
x+y3=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x+y5=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
x+y7=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
x+y1=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B x+y5=0


SS=(5+3)2+(6+2)2=82
SS=2ae=82
a=22 (e=2)
ae=2=OF
SF=422=32
Since, slope of axis SS=2635=1
slope of directrix =1
Equation of directrix is given by y=x+c
y+xc=0
Now, 32=5+6c2 (perpendicular distance of a point from a line)
|11c|=6
11c=±6
c=5 or c=17
Hence, Equation of Directrix can be x+y5=0 or x+y17=0
centre(O)(1,2)
we know that centre and focus lies on opposite side to the directrix. But for x+y17=0, centre(O) and focus(S) lies on the same side.Therefore x+y17=0 is rejected.
Equation of directrix corresponding to focus S is x+y5=0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Hyperbola and Terminologies
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon