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2 years ago

Find the equation of the parabola with focus (2, 3) and directrix y = -1. es

Mathematics

2 answers:

aev [14]2 years ago

7 0

Y=1/8^2-1/2x + 3/2 would be the answer

Elan Coil [88]2 years ago

4 0

Answer:

Below in bold.

Step-by-step explanation:

Let (x, y) be a point on the parabola. As the graph is a parabola, the distance of this point to the focus is equal to the distance of this point from the directrix. So:

√(( x - 2)^2 + (y - 3)^2) = y - (-1)

Squaring both sides:

(x - 2)^2 + (y - 3)^2 = (y + 1)^2

x^2 - 4x + 4 + y^2 - 6y + 9 = y^2 + 2y + 1

x^2 - 4x + 4 + 9 - 1 = 2y + 6y

8y = x^2 - 4x + 12

y = 1/8(x^2 - 4x + 12)

or we can write it as

y = 1/8x^2 - 1/2 x + 3/2.

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the sides of a rectangle are the ratio 2:5. (for every 2cm of the width, the length is 5cm) the perimeter of the rectangle is 70

viva [34]

------------------------------------------------------------------------------------
Ratio
------------------------------------------------------------------------------------
Width : Length
2 : 5

Let x be the scale factor

Width : Length
2x : 5x

------------------------------------------------------------------------------------
Form equation and solve x
------------------------------------------------------------------------------------
Perimeter = 2(Length + Width)
70 = 2(5x + 2x)
70 = 2(7x)
70 = 14x
14x = 70
x = 5

------------------------------------------------------------------------------------
Find Length and Width
------------------------------------------------------------------------------------
Length = 5x
Length = 5(5)
Length = 25

Width = 2x
Width = 2(5)
Width = 10

------------------------------------------------------------------------------------
Answer: Length = 25 cm, Width = 10 cm
------------------------------------------------------------------------------------

4 0

3 years ago

How many times does 3 go into 136 mixed fraction

lys-0071 [83]

Answer:

14 times

Step-by-step explanation:

8 0

2 years ago

PLEASE HELP TY OMG TYTYTY

Naya [18.7K]

Answer:

-14x

Step-by-step explanation:

To put in simple terms, this question is asking what -2x+-12x is. To solve this you must add -2 and -12. So... -2+-12=-14. Then add the one "x" at the end.

7 0

3 years ago

Solve the simultaneous equation<br>x2+y2= 26<br>X - Y = 4<br>

gayaneshka [121]

The answer is X=1, y=5. X=-5 y=-1

5 0

3 years ago

What is the approximate distance from the origin to the point (3, −4, 5)? Round to the nearest unit. 4 units 7 units 8 units 9 u

Dafna11 [192]

Answer:

Option B is correct.

Step-by-step explanation:

The distance formula used is:

$d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1})^2}$

We need to find distance between origin and other point (3,-4,5)

Origin is: (0,0,0)

x₁ = 0, y₁ = 0, z₁ =0 and x₂= 3, y₂= -4 and z₂ = 5

Putting values in the distance formula we get:

$d=\sqrt{(3-0)^2+(-4+0)^2+(5-0)^2}\\d=\sqrt{(3)^2+(-4)^2+(5)^2}\\d=\sqrt{9+16+25}\\d=\sqrt{50}\\d=7$

The Distance from the origin to the point (3, −4, 5) is 7 units.

Option B is correct.

3 0

3 years ago