Differential Equations Question 137
Question: The slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes though the point (4, 3). The equation of the curve is
Options:
A) $ x^{2}=y+5 $
B) $ y^{2}=x-5 $
C) $ y^{2}=x+5 $
D) $ x^{2}=y-5 $
Show Answer
Answer:
Correct Answer: C
Solution:
Accordingly $ \frac{dy}{dx}=\frac{1}{2y} $
Therefore $ 2ydy=dx $
Integrating, we get $ y^{2}=x+c $
This passes through $ (4,3) $ , \ $ 9=4+c $
Therefore $ c=5 $
Hence the equation of the curve is $ y^{2}=x+5 $ .
BETA
