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3 years ago

Given the information below, write the equation in Standard Form.

Mathematics

1 answer:

Sergio [31]3 years ago

3 0

Answer:

The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)

Step-by-step explanation:

The standard form of the equation of a parabola is (y - k)² = 4p (x - h), where

The vertex of the parabola is (h , k)
The focus is (h + p, k)

∵ The vertex of the parabola is (3 , -2)

∴ h = 3 and k = -2

∵ The focus is (5 , -2)

∴ h + p = 5

- Substitute h by 3 to find p

∵ 3 + p = 5

- Subtract 3 from both sides

∴ p = 2

∵ The standard form of the equation of the parabola is (y - k)² = 4p (x - h)

- Substitute the values of h , k , and p in the equation

∴ (y - -2)² = 4(2) (x - 3)

∴ (y + 2)² = 8 (x - 3)

The standard form of the equation of the parabola is (y + 2)² = 8 (x - 3)

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Yakvenalex [24]

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3 years ago

A new youth sports center is being built in a safe harbor. The perimeter of the rectangular playing field is 510 yards. The leng

podryga [215]

Answer:

<h2>L=203 yards</h2><h2>W=52 yards</h2>

Step-by-step explanation:

Step one:

given data

perimeter= 510 yards

let the width be x, width=x

length= (4x-5)-----quadruple mean 4 times

Step two:

the expression for perimeter is

P=2L+2W

510=2(4x-5)+2x

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510+10=8x+2x

520=10x

divide both sides by 10

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3 years ago

7- a. What is the radius of the circle with center (3,10) that passes through (12,12)?

loris [4]

Answer: a. Radius of circle = $\sqrt{85}$

b. The equation of this circle : $(x-3)^2+(y-10)^2=85$

Step-by-step explanation:

Given : Center of the circle = (3,10)

Circle is passing through (12,12).

a. To find the radius we apply distance formula (∵ Radius is the distance from center to any point ion the circle.)

Radius of circle = $\sqrt{(12-3)^2+(12-10)^2}$

Radius of circle = $\sqrt{(9)^2+(2)^2}=\sqrt{81+4}=\sqrt{85}$

i.e. Radius of circle = $\sqrt{85}$

b. Equation of a circle = $(x-h)^2+(y-k)^2=r^2$ , where (h,k)=Center and r=radius of the circle.

Put the values of (h,k)= (3,10) and r= $\sqrt{85}$ , we get

$(x-3)^2+(y-10)^2=(\sqrt{85})^2$

$(x-3)^2+(y-10)^2=85$

∴ The equation of this circle : $(x-3)^2+(y-10)^2=85$

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