CircleEasy
Question
The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is
Options
A.(x - 2)y′2 = 25 - (y - 2)2
B.(y - 2)y′2 = 25 - (y - 2)2
C.(y - 2)2y′2 = 25 - (y - 2)2
D.(x - 2)2y′2 = 25 - (y - 2)2
Solution
(x - h)2 + (y - 2)2 = 25 ......(i)
⇒ 2(x - h) + 2(y - 2)
⇒ (x - h) = - (y - 2)
substituting in (1), we have
(y - 2)2
+ (y - 2)2 = 25
(y - 2)2y′2 = 25 - (y - 2)2.c
⇒ 2(x - h) + 2(y - 2)
⇒ (x - h) = - (y - 2)
substituting in (1), we have
(y - 2)2
+ (y - 2)2 = 25(y - 2)2y′2 = 25 - (y - 2)2.c
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