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

x=1 is the radical axis of two circles which cut each other orthogonally. lf x2+y2=9 is the equation of one circle, then the equation of the other circle is

A
x2+y29x+9=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
x2+y2+18x9=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x2+y218x+9=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
x2+y2+9x+9=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C x2+y218x+9=0
Given that x=1 is radical axis of two circles. Therefore the line joining centers should be perpendicular to x=1
Since the center of one circle is (0,0) , the center of another circle should lie on y=0
Let the center of another circle be (a,0) and the radius be r
The equation of circle is (xa)2+y2=r2
Given that the two circles are orthogonal,
We get a2=r2+9
here the centers of two circles are (0,0) and (a,0), radius of two circles are 3 and r respectively.
Since the length of tangents from radical axis are equal, we get (1a)2+0r2=19
a2r2=2a9
We know that a2r2=9 from orthogonal condition
By solving both equations, we get a=9 and r2=72
Therefore the equation of required circle will be x2+y218x+9=0
So the correct option is C

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