The trajectories orthogonal to $(2 a - x) y^{2} = x^{3}$ is:

x^{2} + y^{2} = C (y^{2} + 2 x^{2})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(x^{2} + y^{2})^{2} = C x y

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(x^{2} + y^{2})^{2} = C (y^{2} + 2 x^{2})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(x^{2} + y^{2}) = x^{3} + x y^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $(x^{2} + y^{2})^{2} = C (y^{2} + 2 x^{2})$
$(2 a - x) y^{2} = x^{3}$
Differentiating w.r.t x
$(2 a - x) 2 y \frac{d y}{d x} + y^{2} = 3 x^{2}$
$∴ \frac{d y}{d x} = \frac{3 x^{2} + y^{2}}{2 y (2 a - x)}$
Replacing $\frac{d y}{d x} \to - \frac{d x}{d y}$
$- \frac{d x}{d y} = \frac{3 x^{2} + y^{2}}{2 y (2 a - x)} \Rightarrow - d x (2 a - x) y = d y (3 x^{2} + y^{2}) \Rightarrow {(x^{2} + y^{2})}^{2} = C (y^{2} + 2 x^{2})$

Suggest Corrections

Similar questions

The orthogonal trajectory of y^{2} = 4 ax is

x^{2} - y^{2} = a^{2}

45^{\circ}

2 x^{2} - 8 x y + 7 y^{2} - 8 x y^{2}, 2 y^{2}, 6 x y^{2} - y^{2} + 3 x^{2}, 4 y^{2} - x y - x^{2} + x y^{2}

(x + y) + (x^{2} + x y + y^{2}) + (x^{3} + x^{2} y + x y^{2} + y^{3}) + . . . n

=

(x + y) + (x^{2} + x y + y^{2}) + (x^{3} + x^{2} y + {x y}^{2} + y^{3}) + . . .

n

Join BYJU'S Learning Program