Respuesta :
Answer:
The matched options to the given problem is below:
Step1: Choose a point on the parabola
Step2: Find the distance from the focus to the point on the parabola.
Step3: Use (x, y).
Find the distance from the point on the parabola to the directrix.
Step4: Set the distance from focus to the point equal to the distance from directrix to the point.
Step5: Square both sides and simplify.
Step6: Write the equation of the parabola.
Step by step Explanation:
Given that the focus (-1,2) and directrix x=5
To find the equation of the parabola:
By using focus directrix property of parabola
Let S be a point and d be line
focus (-1,2) and directrix x=5 respectively
If P is any point on the parabola then p is equidistants from S and d
Focus S=(-1,2), d:x-5=0
Step1: Let P(x,y) be any point on parabola
Step2: Therefore the [tex]d=\sqrt{(x+1)^2+(y-2)^2}\hfill (1)[/tex]
Step3: The perpendicular distance from p to d is
[tex]\frac{|x-5|}{\sqrt{(-1)^2+2^2}}[/tex]
[tex]=\frac{|x-5|}{\sqrt{5}}\hfill (2)[/tex]
Step4: equating (1) and (2)
[tex]\sqrt{(x+1)^2+(y-2)^2}=\frac{|x-5|}{\sqrt{5}}[/tex]
Step5: squaring on both sides
[tex](x+1)^2+(y-2)^2=\frac{|x-5|^2}{5}[/tex]
[tex]5[(x+1)^2+(y-2)^2]=(x-5)^2[/tex]
[tex]5[x^2+2x+1+y^2-2y+4-x^2+10x-25]=0[/tex]
[tex]12x+y^2-2y-24=0[/tex]
Step6: Equation of the parabola is
[tex]y^2-2y+12x-24=0[/tex]
