Question

MEDAL!!!!!!
What is the equation of a parabola with vertex at (1, −3) and focus at (−2, −3)?

Answer 1

I am aware of the formula of parabola and how to find the focus,directrix etc.

Answer 2

@TuringTest

Answer 3

@Data_LG2

Answer 4

notice the vertex
notice the focus

how many units is the focus from the vertex?

Answer 5

-4, 6

Answer 6

?

Answer 7

@jdoe0001
3 units

Answer 8

\[(y+3)^{2}=-12(x-1)\]is what I get.

Answer 9

that means the parabola opens sideways, to the left

Answer 10

agreed

Answer 11

so is 3 units from the vertex to the focus, or "p" distance

a horizonal parabola the left means, "y" is squared and "p" is negative

thus \(\bf (y-{\color{blue}{ k}})^2=4{\color{brown}{ p}}(x-{\color{blue}{ h}})\qquad vertex \ (1,-3)\quad p=-3
\\ \quad \\
(y-{\color{blue}{ (-3)}})^2=4{\color{brown}{ -3}}(x-{\color{blue}{ 1}})\implies (y+{\color{blue}{ (3)}})^2=4{\color{brown}{ -3}}(x-{\color{blue}{ 1}})\)

Answer 12

hmhm well so \(\bf (y-{\color{blue}{ k}})^2=4{\color{brown}{ p}}(x-{\color{blue}{ h}})\qquad vertex \ (1,-3)\quad p=-3
\\ \quad \\
(y-{\color{blue}{ (-3)}})^2=4{\color{brown}{ (-3)}}(x-{\color{blue}{ 1}})\implies (y+{\color{blue}{ (3)}})^2=12(x-{\color{blue}{ 1}})\)

Answer 13

well. -12 dohh.. the parabola opens to the left ... so \(\bf (y-{\color{blue}{ k}})^2=4{\color{brown}{ p}}(x-{\color{blue}{ h}})\qquad vertex \ (1,-3)\quad p=-3
\\ \quad \\
(y-{\color{blue}{ (-3)}})^2=4{\color{brown}{ (-3)}}(x-{\color{blue}{ 1}})\implies (y+{\color{blue}{ (3)}})^2=-12(x-{\color{blue}{ 1}})\)