The equation of the parabola whose vertex and focus lie on the $x$-axis at distances $a$ and $a'$ from the origin,respectively,is
- A$y^2 = 4(a' - a)(x - a)$
- B$y^2 = 4(a' - a)(x + a)$
- C$y^2 = 4(a' + a)(x - a)$
- D$y^2 = 4(a' + a)(x + a)$
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For the parabola $y^2+6y-2x+5=0$,match the items in List-$I$ with the suitable item in List-$II$ given below:
List-$I$ (Geometric Property) List-$II$ (Coordinates/Equations) $I$. Vertex $A$. $\left(-\frac{3}{2}, -3\right)$ $II$. Focus $B$. $\left(\frac{3}{2}, -3\right)$ $III$. Equation of the directrix $C$. $2x + 5 = 0$ $IV$. Equation of the axis $D$. $2x + y + 3 = 0$ $E$. $y + 3 = 0$ $F$. $(-2, -3)$
The correct matching is:
| List-$I$ (Geometric Property) | List-$II$ (Coordinates/Equations) |
|---|---|
| $I$. Vertex | $A$. $\left(-\frac{3}{2}, -3\right)$ |
| $II$. Focus | $B$. $\left(\frac{3}{2}, -3\right)$ |
| $III$. Equation of the directrix | $C$. $2x + 5 = 0$ |
| $IV$. Equation of the axis | $D$. $2x + y + 3 = 0$ |
| $E$. $y + 3 = 0$ | |
| $F$. $(-2, -3)$ |
The correct matching is:
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