JEE Main · 2008 · 27 Apr 2008 · Offline · Differential Equations

The differential equation of the family of circles with fixed radius 5 units and centre on the line

y = 2

Answer: (C)

Solution

A circle of radius

5

centred on the line

y = 2

has equation

(x - h)^{2} + (y - 2)^{2} = 25

with

h

the only parameter. Differentiating,

2 (x - h) + 2 (y - 2) y^{'} = 0

, so

x - h = - (y - 2) y^{'}

. Substituting back to eliminate

h

gives

(y - 2)^{2} y^{'2} + (y - 2)^{2} = 25

, that is

(y - 2)^{2} y^{'2} = 25 - (y - 2)^{2}

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option

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