Parametric Equation of a Parabola

Q.

Find the equation for the ellipse that satisfies the given conditions,
Foci $(\pm 3,0)a=4$

Q.

The locus of the centres of the circles which cut the circles $x^2+y^2+4x-6y+9=0and{x}^2+y^2-5x+4y-2=0$ orthogonally is

1. x - y + 2 = 0

2. 9x + 10y - 7 = 0

3. 9x - 10y + 11 = 0

4. 9x + 10y + 7 = 0

Q. Match the following with the parametric equation of the parabola:

1. $x=a{t}^2,y=2at$
2. $x=-a{t}^2,y=2at$
3. $x=2at,y=a{t}^2$
4. $x=2at,y=-a{t}^2$

Q. Find the parametric equation of the parabola $(x-1{)}^2=-12(y-2)$

Q.

Which of the following can be the parametric equation of $x^2=4ay$

1. (at², 2at)

2. (2at, at²)

3. (-2at, at²)

4. (at², -2at)

Q. If a parabola reflector with its axis as $x-axis$ is $20$ cm in diameter and $5$ cm deep. Find the focus.

Q.

Which of the following can be the parametric equation of
$(x-1{)}^2=-36(y-4)$

1. $x=1+18t$ and$y=4-9t^2$

2. $x=-1+18t$ and$y=-4-9t^2$

3. $x=-1-18t$ and $y=4-9t^2$

4. $x=1+18t$ and $y=-4-9t^2$

Q.

Match the following equation of parabola

$\begin{array}{cc}\text{Parabola}& \text{parametric equation}\\ \text{N)}{x}^2=4ay& \text{1)}(a{t}^2,2at)\\ \text{E)}{y}^2=4ax& \text{2)}(-at,2at)\\ \text{W)}{y}^2=-4ax& \text{3)}(2at,a{t}^2)\\ \text{S)}{x}^2=-4ay& \text{4)}(2at,a{t}^2)\end{array}$

1. N-2, E-3, W-1, S - 4

2. N-4, E-1, W-2, S - 3

3. N-1, E-3, W-2, S - 4

4. N-3, E-1, W-2, S - 4