Family of Curves

Q.

Find the equation of the parabola that satisfies the given conditons:
Focus
Vertex (0, 0) passing trhough (5, 2) and symmetric with respect to y - axis.

Q.

Find the equation of the parabola that satisfies the given conditons:
Focus (0, -3); Directrix y = 3

Q.

Find the equation of the parabola that satisfies the given conditons:
Focus
Vertex (0, 0) passing through (2, 3) and axis is along x - axis.

Q.

ind teh coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
$x^2=6y$

Q.

Find the equation of the parabola that satisfies the given conditons:
Focus
Vertex (0, 0); Focus (3, 0)

Q.

Find the equation of the hyperbola satisfying the given conditions.
Foci $(0,\pm 13),$ the conjugate axis is of lenth 24.

Q. The differential equation of all circles which pass through the origin and whose centers lie on the y-axis is

1. $(x^2-y^2)\frac{dy}{dx}-2xy=0$
2. $(x^2-y^2)\frac{dy}{dx}+2xy=0$
3. $(x^2-y^2)\frac{dy}{dx}-xy=0$
4. $(x^2-y^2)\frac{dy}{dx}+xy=0$

Q.

Find the equation of the parabola that satisfies the given conditons:
Focus (6, 0); directrix x = -6

Q. Differential equation of the family of parabolas whose vertex lie on the $x-$ axis and focus as origin is

1. $y{\left(\frac{dy}{dx}\right)}^2+2x\frac{dy}{dx}-y=0$
2. $y{\left(\frac{dy}{dx}\right)}^2+2x\frac{dy}{dx}+y=0$
3. $y{\left(\frac{dy}{dx}\right)}^2+x\frac{dy}{dx}-y=0$
4. $y{\left(\frac{dy}{dx}\right)}^2+x\frac{dy}{dx}+y=0$