1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The common tangent to the circles x2+y2−6x=0 and x2+y2+2x=0 forms

A
Right angle triangle
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
isosceles triangle
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Right angle isosceles triangle
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Equilateral triangle
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D Equilateral triangle Given circles are x2+y2−6x=0 Centre C1=(3,0) and radius r1=3 x2+y2+2x=0 Centre C2=(−1,0) and radius r2=1 ∵C1C2=r1+r2 Number of common tangents possible are 3. I and E divides C1 and C2 in ratio 1:3 internally and externally. So, I=(1(3)+3(−1)4,1(0)+3(0)4) =(0,0) E=(1(3)−3(−1)−2,1(0)−3(0)−2) =(−3,0) For Direct common tangent, y−0=m(x+3) ⇒mx−y+3m=0 Perpendicular distance = Radius ⇒∣∣∣2m√1+m2∣∣∣=1 ⇒4m2=m2+1 ⇒m=±1√3 So, inclination of direct common tangents are 30∘ and 150∘ It can be observed that in △EAB, ∠E=∠A=∠B=60∘. So, it is equilateral triangle.

Suggest Corrections
0
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program