Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
The standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin and directrix is y² = 16x.
What is the parabola?
It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
Given that the parabola's vertex is located at the origin and that the directrix is at x = -4, the focus is at (4,0).
Then the equation can be written as
[tex]\rm \sqrt{(x-4)^2 +(y-0)^2} = \sqrt{(x+4)^2 + (y-y)^2}\\\\\sqrt{(x-4)^2 +(y-0)^2} = \sqrt{(x+4)^2}[/tex]
On squaring both sides, we have
[tex]\begin{aligned} (x-4)^2 +(y-0)^2 &= (x+4)^2 \\\\x^2 + 16 - 8x +y^2 &= x^2 + 16 + 8x\\\\y^2 &= 16x \end{aligned}[/tex]
More about the parabola link is given below.
https://brainly.com/question/8495504
#SPJ4
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
