The slope of a curve at any point is the reciprocal of twice of the ordinate at the point and it passes through the point (4,3). The equation of the curve is -

  • Option 1)

    x^{2}=y+5

  • Option 2)

    y^{2}=x-5

  • Option 3)

    y^{2}=x+5

  • Option 4)

    x^{2}=y-5

 

Answers (1)

use the concept

Solution of Differential Equation -

\frac{\mathrm{d}y }{\mathrm{d} x} =f\left ( ax+by+c \right )

put

 Z =ax+by+c

 

 

- wherein

Equation with convert to

\int \frac{dz}{bf\left ( z \right )+a} =x+c

 

 

 

 \frac{dy}{dx}=\frac{1}{2y}\:(given)

\int 2ydy=\int dx

\frac{2y^{2}}{2}=x+C

y^{2}=x+C

9=4+C   

\therefore C=5

y^{2}-5=x

y^{2}=x+5


Option 1)

x^{2}=y+5

Option is incorrect

Option 2)

y^{2}=x-5

Option is incorrect

Option 3)

y^{2}=x+5

Option is correct

Option 4)

x^{2}=y-5

Option is incorrect

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