Guys i am struggling so much, two questions

1. the directrix of a parabola is x = 0. its focus is (2,6) .
what is the standard form of the parabola?
2. the vertex of a parabola is (−5,2) , and its focus is (−5,6) .
what is the standard form of the parabola?

the equation of the standard parabola

1)

The equation of the standard parabola

2) (x+5)^2 = 16(y-2)

Step-by-step explanation:

Explanation

Parabola:-

The set of points in a plane whose distance from a fixed point and a constant ratio to their corresponding perpendicular distance from a fixed straight line is a conic.

Let S be a fixed point and l be a fixed straight line from any point P,the perpendicular PM is drawn to the line 'l'

1) Step 1 :-

Given the focus   S = (2,6) and directrix is x=0

we know that

now cross multiplication , we get

squaring on both sides,we get

step 2:-

now using distance formula is

Given S =(2,6) and P(x,y) be any point on parabola

........(1)

Now using perpendicular distance formula

let P(x , y ) be any point on the parabola

Given the directrix is x =0 and P(x,y) be any point on parabola

......(2)

equating equation(1) and equation (2), on simplification

we get .....(3)

now the equation (3) is

now the standard form of parabola is

Final answer:-

2) Explanation:-

step 1:

Given vertex of a parabola is A(-5,2) and its focus is S(-5,6)

here the given points of 'x'co- ordinates are equal

now the standard equation of parabola

now you have to find' a' value

Given vertex of a parabola is A(-5,2) and its focus is S(-5,6)

The distance of

 on simplification we get a =4

Final answer :-

the vertex (h,k) = (-5,2) and a=4

The standard parabola is

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950