Consider a circle x squared plus y squared minus 4 x minus 6 y plus 11 space equals space 0 if m1 and m2 are the max and min values of
x / y      for all ordered pairs (x,y) on the circumference of the circle, then the value of m1 + m2 is ____ ?.
 
 

Asked by Sunil Soni | 10th Aug, 2016, 05:40: PM

Expert Answer:

begin mathsize 20px style F r o m space t h e space e q u a t i o n space w e space c a n space s e e space t h a t space t h e space g i v e n space c i r c l e space h a s space i s space c e n t r e d space a t
open parentheses 2 comma 3 close parentheses space a n d space r a d i u s space square root of 2
a s
open parentheses x minus 2 close parentheses squared plus open parentheses y minus 3 close parentheses squared equals space 2
i s space t h e space e q u a t i o n space o f space t h e space c i r c l e space w h e n space w e space c l u b space t h e space t e r m s space i n space p e r f e c t space s q u a r e.
f r o m space t h e space f i g u r e space w e space c a n space s e e space t h a t space t h a space m a x i m u m space a n d space t h e space m i n i m u m space v a l u e space o f space t h e space
x over y space o n space t h e space c i r c u m f e r e n c e space c a n space b e space P comma Q comma X space o r space Y
T o space c h e c k space w h i c h space i s space t h e space m i n i m u m space w e space t r y space t o space f i n d space o u t space t h e space v a l u e s space o f space t h e s e space p o i n t s space a s
P left parenthesis 2 comma space 3 plus square root of 2 right parenthesis rightwards double arrow x over y equals fraction numerator 2 over denominator 3 plus square root of 2 end fraction almost equal to space 0.45
Q left parenthesis 2 plus square root of 2 comma 3 right parenthesis rightwards double arrow x over y equals space fraction numerator 2 plus square root of 2 over denominator 3 end fraction space almost equal to 1.13
X open parentheses 2 comma 3 minus square root of 2 close parentheses rightwards double arrow x over y equals fraction numerator 2 over denominator 3 minus square root of 2 end fraction almost equal to 1.261
Y open parentheses 2 minus square root of 2 comma 3 close parentheses rightwards double arrow x over y equals fraction numerator 2 minus square root of 2 over denominator 3 end fraction almost equal to 0.195
H e n c e space t h e space m a x i m u m space i s space p o i n t space X space a n d space m i n i m u m space i s space p o i n t space Y space
n o w space w e space c a n space e a s i l y space f i n d space t h e space a n s w e r. end style

Answered by Tripti Agrawal | 12th Aug, 2016, 02:27: PM