Question

Match the steps to find the equation of the parabola with focus (-1, 2) and directrix x = 5.

Answer 1

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 $d=\sqrt{(x+1)^2+(y-2)^2}\hfill (1)$

Step3: The perpendicular distance from p to d is

$\frac{|x-5|}{\sqrt{(-1)^2+2^2}}$

$=\frac{|x-5|}{\sqrt{5}}\hfill (2)$

Step4: equating (1) and (2)

$\sqrt{(x+1)^2+(y-2)^2}=\frac{|x-5|}{\sqrt{5}}$

Step5: squaring on both sides

$(x+1)^2+(y-2)^2=\frac{|x-5|^2}{5}$

$5[(x+1)^2+(y-2)^2]=(x-5)^2$

$5[x^2+2x+1+y^2-2y+4-x^2+10x-25]=0$

$12x+y^2-2y-24=0$

Step6: Equation of the parabola is

$y^2-2y+12x-24=0$