We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

#1**+3 **

The vertex is ( 5, [13 + 2]/2 ) = (5, 7.5)

p is the distance from the vertex to the focus = 7.5 - 2 = 5.5

The parabola turns downward because the directrix is above the focus

We have the form :

4p ( y - k)^2 = - (x - h)^2 wher (h, k) = the vertex....so we have

4(5.5) (y - 7.5) = - (x - 5)^2 simplify

22(y - 7.5) = - ( x - 5)^2 divide both sides by 22

y - 7.5 = -(1/22)(x - 5)^2 add 7.5 to both sides

y = -(1/22)(x - 5)^2 + 7.5

Here is a graph : https://www.desmos.com/calculator/a8n6hmiw4w

CPhill Feb 26, 2019

#2**+2 **

CPhill is working on this...I know he does this differently than what I am going to show ya....

Definition of parabola is the set of points that are equidistant from a point called the focus and a line called the directrix.

This parabola has the focus BELOW the directrix, so it opens downward....it looks like a dome.

Point x,y on the parabola has the same distance to the focus and the line y= 13

Distance to the focus is (x-5)^2 +(y-2)^2 = d^2

Distance to the directrix is simply d = 13-y d^2 = (13-y)^2 these two d^2 are equal

so

(x-5)^2 + (y-2)^2 = (13-y)^2 Expand and simplify to find your parabola equation

x^2 - 10x + 25 + y^2 - 4y + = y^2 -26y + 169 gather like terms and simplify and you will get

y = -1/22 x^2 + 10/22 x + 140/22 for your parabola

...here is a graph..... Well...you can look at CPHill's graph !

ElectricPavlov Feb 26, 2019