A circle x2+y2+4x−22y+c=0 is the director circle of circle S1 and S2 is the director circle of circle S1 and so on. If the sum of radii of all these circles is 2, then the value of C is ........

Given circle x2+y2+4x−22y+c=0radius=6-c=a(let) Now radius of S1=a2 radius of S2=a2 and so on Given that a+a2+a2+......+∞=2 ⇒a(11-12)=2 ⇒2a2-1=2 ⇒a=2-2=6-c squaring on both sides 4+2-42=6-c ⇒c=42

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A circle $x^{2} + y^{2} + 4 x - 2 \sqrt{2} y + c = 0$ is the director circle of circle S₁ and S₂ is the director circle of circle S₁ and so on. If the sum of radii of all these circles is 2, then the value of C is ........

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 5.6.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given circle $x^{2} + y^{2} + 4 x - 2 \sqrt{2} y + c = 0$

$r a d i u s = \sqrt{6 - c} = a (l e t) N o w r a d i u s o f S_{1} = \frac{a}{\sqrt{2}} r a d i u s o f S_{2} = \frac{a}{2} a n d s o o n G i v e n t h a t a + \frac{a}{\sqrt{2}} + \frac{a}{2} + . . . . . . + \infty = 2 \Rightarrow a (\frac{1}{1 - \frac{1}{\sqrt{2}}}) = 2 \Rightarrow \frac{\sqrt{2} a}{\sqrt{2} - 1} = 2 \Rightarrow a = 2 - \sqrt{2} = \sqrt{6 - c} s q u a r i n g o n b o t h s i d e s 4 + 2 - 4 \sqrt{2} = 6 - c \Rightarrow c = 4 \sqrt{2}$