Question

5. Find the equation of Parabola whose directrix is x+3=0​

Answer 1

Answer:

Answer:

x=0-3

x=-3 is the answer

Answer 2

The complete question is "Find the equation of the parabola with the focus (3,0) and directrix x+3=0."

The equation of the parabola with focus (3,0) and directrix x+3=0 is $y^{2} =12x$

Step-by-step explanation:

From the definition of parabola, we have

PS=PM where S is the focus, M is the directrix and P is any point on parabola.

Suppose that P is (x,y)

PS=PM

Square on both sides.

$\Rightarrow \text{P}{{\text{S}}^{2}}=\text{P}{{\text{M}}^{2}}$

$\Rightarrow {{(\text{x}-3)}^{2}}+{{(\text{y}-0)}^{2}}={{\left| \frac{\text{x}+3}{\sqrt{{{1}^{2}}+{{0}^{2}}}} \right|}^{2}}$

Simplify and solve it.

$\Rightarrow {{\text{x}}^{2}}-6\text{x}+9+{{\text{y}}^{2}}={{\text{x}}^{2}}+6\text{x}+9$

$\Rightarrow {{\text{y}}^{2}}=12\text{x}$

Hence, the equation of the parabola with focus (3,0) and directrix x+3=0 is $y^{2} =12x$