At FocusMods.com™ we sell performance parts, accessories and mods for the Ford Focus ST, Ford Focus RS, Ford Focus ZX3, Ford Focus SVT, Ford Focus 1.0 Ecoboost, Fiesta 1.0 Ecoboost and Fiesta ST. We are passionate about turbocharged cars, hot hatches and anything Focus! Furthermore, we have over ten years of professional experience in modifying and tuning cars.

Are you looking for more power from your RS or ST? We have the answer! Turbocharged cars love when you open up their factory exhausts with a new cat back system. They also thrive when restrictive factory air boxes are replaced with free flowing air intake systems. In addition to that, we recommend adding a computer tuner from COBB or SCT to electronically tie everything together! Want more information, or a modification plan for your car? Contact us!

Remember, here at FocusMods.com™, we're authorized dealers for Magnaflow, COBB Tuning, MBRP, SCT and several other great brands. In fact, we offer an assorted collection of exhaust systems, intake systems, computer tuners, blow off valves, intercoolers, coilovers, springs and wastegates. So, if you're looking for more power, better handling, enhanced performance and a more enjoyable drive – we have the mods that you need!

Rating applies to 2012-18 models. Tested vehicle: 2012 Ford Focus SE 4-door with standard front and rear head curtain airbags and standard front seat-mounted torso airbags The Ford Focus 4-door was redesigned for the 2012 model year. The side ratings also apply to the 4-door hatchback version of the Focus, also redesigned for the 2012 model year. 4.9/5.0 Satisfaction Rating over the last 100,000 sessions.See complete details for Better Score Guarantee. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. Award-Winning claim based on CBS Local and Houston Press awards. Focus 11 is the fourteenth studio album by Dutch progressive rock band Focus, released in November 2018 on In and Out of Focus Records.It is their first album to feature bassist Udo Pannekeet, who replaced Bobby Jacobs in 2016. Track listing 'Who's Calling?' (Thijs van Leer) – 5:27 'Heaven' (van Leer) – 4:26 'Theodora Na Na Na' (van Leer) – 4:27 'How Many Miles?' Ford - Focus - Trend, 1.6 Zetec-SE Gasoline, year 2004, 74 kW (101 PS), manual.

Given the focus and directrix of a parabola , how do we find the equation of the parabola?

If we consider only parabolas that open upwards or downwards, then the directrix will be a horizontal line of the form $y=c$ .

Let $\left(a,b\right)$ be the focus and let $y=c$ be the directrix. Let $\left(x_0,y_0\right)$ be any point on the parabola.

Any point, $\left(x_0,y_0\right)$ on the parabola satisfies the definition of parabola, so there are two distances to calculate:

1. Distance between the point on the parabola to the focus
2. Distance between the point on the parabola to the directrix

To find the equation of the parabola, equate these two expressions and solve for $y_0$ .

Find the equation of the parabola in the example above.

Distance between the point $\left(x_0,y_0\right)$ and $\left(a,b\right)$ :

$\sqrt{{\left(x_0-a\right)}^2+{\left(y_0-b\right)}^2}$

Distance between point $\left(x_0,y_0\right)$ and the line $y=c$ :

$y_0-c$

(Here, the distance between the point and horizontal line is difference of their $y$ -coordinates.)

Equate the two expressions.

$\sqrt{{\left(x_0-a\right)}^2+{\left(y_0-b\right)}^2}=y_0-c$

Square both sides.

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${\left(x_0-a\right)}^2+{\left(y_0-b\right)}^2={\left(y_0-c\right)}^2$

Expand the expression in $y_0$ on both sides and simplify.

${\left(x_0-a\right)}^2+b^2-c^2=2\left(b-c\right)y_0$

This equation in $\left(x_0,y_0\right)$ is true for all other values on the parabola and hence we can rewrite with $\left(x,y\right)$ .

Therefore, the equation of the parabola with focus $\left(a,b\right)$ and directrix $y=c$ is

${\left(x-a\right)}^2+b^2-c^2=2\left(b-c\right)y$

Example:

If the focus of a parabola is $\left(2,5\right)$ and the directrix is $y=3$ , find the equation of the parabola.

Let $\left(x_0,y_0\right)$ be any point on the parabola. Find the distance between $\left(x_0,y_0\right)$ and the focus. Then find the distance between $\left(x_0,y_0\right)$ and directrix. Equate these two distance equations and the simplified equation in $x_0$ and $y_0$ is equation of the parabola.

The distance between $\left(x_0,y_0\right)$ and $\left(2,5\right)$ is $\sqrt{{\left(x_0-2\right)}^2+{\left(y_0-5\right)}^2}$

The distance between $\left(x_0,y_0\right)$ and the directrix, $y=3$ is

$y_0-3$ .

Equate the two distance expressions and square on both sides.

$\sqrt{{\left(x_0-2\right)}^2+{\left(y_0-5\right)}^2}=y_0-3$

${\left(x_0-2\right)}^2+{\left(y_0-5\right)}^2={\left(y_0-3\right)}^2$

Simplify and bring all terms to one side:

$x_0{2}^{}-4x_0-4y_0+20=0$

Write the equation with $y_0$ on one side:

$y_0=\frac{x_0{2}^{}}{4}-x_0+5$

This equation in $\left(x_0,y_0\right)$ is true for all other values on the parabola and hence we can rewrite with $\left(x,y\right)$ .

So, the equation of the parabola with focus $\left(2,5\right)$ and directrix is $y=3$ is

1 Equals 0

$y=\frac{x^2}{4}-x+5$