    Question

# For the circles S1≡x2+y2−4x−6y−12=0 and S2≡x2+y2+6x+4y−12=0 and the line L≡x+y=0

A
L is the common tangent of S1 and S2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
L is the common chord of S1 and S2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
L is radical axis of S1 and S2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
L is perpendicular to the line joining the centers of S1 and S2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct options are B L is radical axis of S1 and S2 C L is perpendicular to the line joining the centers of S1 and S2 D L is the common chord of S1 and S2Centre of S1 is C1≡(2,3) and radius of S1 is r1=5.Centre of S1 is C2≡(−3,−2)and radius of S1 is r1=5.Also, d= distance between centres =C1C2=√25+25=√50∴|r1−r2|=0 and r1+r2=10.Since |r1−r2|<C1C2<r1+r2, therefore circles S1 and S2 intersect.Equation of the common chord of C1 and C21 is S1−S2=0 i.e., x+y=0, which is also the equation of the radical axis and hence it is ⊥ to the line joining the centres C1 and C2 of the two circles.  Suggest Corrections  0      Similar questions
Join BYJU'S Learning Program
Select...  Related Videos   Line and a Parabola
MATHEMATICS
Watch in App  Explore more
Join BYJU'S Learning Program
Select...