The equation of the parabola with vertex at $(0,0)$ and length of latus rectum equal to $\frac{16}{3}$ is:
- A$8x^{2} + 3y^{2} = 72$
- B$16y^{2} = 3x$
- C$3y^{2} = 16x$
- D$3x^{2} + 16y^{2} = 48$
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View SolutionFor the parabola $y^2+6y-2x+5=0$,match the items in List-$I$ with the suitable item in List-$II$ given below:
List-$I$ List-$II$ $(I)$ Vertex $(A)$ $(-\frac{3}{2}, -3)$ $(II)$ Focus $(B)$ $(\frac{3}{2}, -3)$ $(III)$ Equation of the directrix $(C)$ $2x+5=0$ $(IV)$ Equation of the axis $(D)$ $2x+y+3=0$ $(E)$ $y+3=0$ $(F)$ $(-2, -3)$
| List-$I$ | List-$II$ |
| $(I)$ Vertex | $(A)$ $(-\frac{3}{2}, -3)$ |
| $(II)$ Focus | $(B)$ $(\frac{3}{2}, -3)$ |
| $(III)$ Equation of the directrix | $(C)$ $2x+5=0$ |
| $(IV)$ Equation of the axis | $(D)$ $2x+y+3=0$ |
| $(E)$ $y+3=0$ | |
| $(F)$ $(-2, -3)$ |
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