If the focus divides a focal chord of the parabola $y^2 = 16x$ into $2$ parts having lengths $a$ and $c$,such that $a, b, c$ are in $H.P.$,then the value of $b$ is equal to:
- A$2$
- B$4$
- C$6$
- D$8$
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If one end of a focal chord of the parabola $y^2=8x$ is $\left(\frac{1}{2}, 2\right)$,then the length of the focal chord is $........$ units.
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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-$I$ (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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