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

If (1,2) is a pole of the circle x2+y210x10y+25=0, then the equation of the diameter which bisects the polar is

A
2x+y15=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
4x7y+15=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x2y+5=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
7x4y15=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 7x4y15=0
Given circle is
x2+y210x10y+25=0
C=(5,5),r=5
Equation of polar when pole is (1,2) is
x2y5(x+1)5(y2)+25=04x7y+30=04x+7y30=0
Distance from centre to polar is
|20+3530|65=2565<5
So, polar is a chord
The diameter which bisects the chord is perpendicular to it, so
7x4y+λ=0
It passes through centre (5,5)
3520+λ=0λ=15

Hence, the required equation of the diameter is
7x4y15=0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon