F i n d space t h e space d i f f e r e n t i a l space e q u a t i o n space o f space t h e space f a m i l y space o f space c i r c l e s space o f space r a d i u s space r space w h o s e
c e n t r e space l i e space o n space t h e space x minus a x i s colon

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Asked by Topperlearning User | 4th Nov, 2016, 07:01: PM

Expert Answer:

L e t space t h e space c e n t r e space b e space left parenthesis h comma 0 right parenthesis
T h e space e q u a t i o n space o f space c i r c l e space i s space g i v e n space b y
left parenthesis x minus h right parenthesis squared plus y squared equals r squared
D i f f e r e n t i a t i n g space w. r. t space x space w e space g e t
2 left parenthesis x minus h right parenthesis plus 2 y fraction numerator d y over denominator d x end fraction equals 0
rightwards double arrow x minus h plus y fraction numerator d y over denominator d x end fraction equals 0
rightwards double arrow h equals x plus y fraction numerator d y over denominator d x end fraction
S u b s t i t u t i n g space h space i n space o r i g i n a l space e q u a t i o n space w e space g e t
left parenthesis x minus x minus y fraction numerator d y over denominator d x end fraction right parenthesis squared plus y squared equals r squared
equals y squared open parentheses fraction numerator d y over denominator d x end fraction close parentheses squared plus y squared equals r squared space i s space t h e space r e q u i r e d space d i f f e r e n t i a l space e q u a t i o n

Answered by  | 4th Nov, 2016, 09:01: PM