Differential Equations Question 127
Question: The differential equation of the family of parabolas with focus at the origin and the x-axis as axis is
[EAMCET 2003]
Options:
A) $ y{{( \frac{dy}{dx} )}^{2}}+4x\frac{dy}{dx}=4y $
B) $ -y{{( \frac{dy}{dx} )}^{2}}=2x\frac{dy}{dx}-y $
C) $ y{{( \frac{dy}{dx} )}^{2}}+y=2xy\frac{dy}{dx} $
D) $ y{{( \frac{dy}{dx} )}^{2}}+2xy\frac{dy}{dx}+y=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
Equation of family of parabolas with focus at $ (0,0) $ and x-axis as axis is $ y^{2}=4a(x+a) $ - ..(i)
Differentiating (i) with respect to x,
$ 2yy_1=4a;y^{2}=2yy_1( x+\frac{yy_1}{2} ) $
$ y=2xy_1+yy_1^{2} $
Therefore $ y{{( \frac{dy}{dx} )}^{2}}+2x\frac{dy}{dx}=y $ .
BETA
