MATHEMATICS HIGH SCHOOL

derive the equation of the parabola with a focus at (4,-7) and a directrix of y=-15. put the equatiom in standard form

Answers

Answer 1

Answer:

Answer:

The equation of the parabola with a focus at (4,-7) and a directrix of y=-15 is $y=(x^(2))/(16)-(x)/(2)-10$

Step-by-step explanation:

we need to drive the equation of the parabola with a focus at ( 4, -7) and a directrix of y= -15

From the given focus ( 4, -7) and equation of directrix y = - 15 calculate p

$p=(1)/(2)(y_0-y)$

where $y_0$ is is ordinate of focus and y is equation of directrix.

$p=(1)/(2)(-7-(-15))$

$p=(1)/(2)(-7+15)$

$p=(1)/(2)(8)$

$p=4$

Calculate the vertex (h,k)

$h=4\; \text{and}\; k=(-7+(-15))/(2)=-11$

vertex (h,k) =(4,-11)

Since, vertex form is :

$(x-h)^(2)=4p(y-k)$ (positive 4p shows it open upward)

$(x-4)^(2)=4(4)(y-(-11))$

$(x-4)^(2)=16(y+11)$

$x^(2)+16-8x=16y+176$

subtract both the sides by 176,

$x^(2)-8x-160=16y$

Divide both the sides in above by 16,

$(x^(2))/(16)-(8x)/(16)-(160)/(16)=y$

$(x^(2))/(16)-(x)/(2)-10=y$

Hence, the equation of the parabola with a focus at (4,-7) and a directrix of y=-15 is $y=(x^(2))/(16)-(x)/(2)-10$

Answer 2

Answer: $\sqrt{(x_(0) - 4)^(2) + (y_(0) - (-7))^(2)} = |y_(0) - (-15)|$
$(\sqrt{(x_(0) - 4)^(2) + (y_(0) + 7)^(2))^(2)} = (y_(0) + 15)^(2)$
$(x_(0) - 4)^(2) + (y_(0) + 7)^(2) = (y_(0) + 15)^(2)$
$(x_(0)^(2) - 8x_(0) + 16) + (y_(0)^(2) + 14y_(0) + 49) = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) + y_(0)^(2) - 8x_(0) + 14y_(0) + 16 + 49 = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) + y_(0)^(2) - 8x_(0) + 14y_(0) + 65 = y_(0)^(2) + 30y_(0) + 225$
$x_(0)^(2) - 8x_(0) - 16y_(0) - 160 = 0$
$16y_(0) = x_(0)^(2) - 8x_(0) - 160$
$(16y_(0))/(16) = (x_(0)^(2) - 8x_(0) - 160)/(16)$
$y_(0) = (1)/(16)x_(0)^(2) - (1)/(2)x_(0) - 10$
$y = (1)/(16)x^(2) - (1)/(2)x - 10$

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How do you make a mix number an improperfraction example 4 8/11

Answers

Basically what you do is you multiply the denominator (11) by the whole number (4). Then, you add that to the numerator (8).

For this one it would be 11 x 4 = 44
44 + 8 = 52

4 8/11
= 4+ 8/11
= 44/11+ 8/11
= 52/11

The final answer is 52/11~

What is the slope of the line represented by the values in the table?y
14
X
10
2
3
7.
20
- 2
0
8
34
- 2
01
2

Answers

Answer:

Undefined

Step-by-step explanation:

If I am seeing the table right, 14 is the only y coordinate and 14 goes with all the x.

so the line would be horizontal

Cylinder has a height of 14 centimeters and its circle bases have a radius of 10 centimeters. find the surface area of the cylinder.2(100  ) + 140   square centimeters
1,400  + 140   square centimeters
2(100  ) + 280   square centimeters
2(1,400  ) + 2(140  ) square centimeters

Answers

200 plus 140 is 300
1400 plus 140 is 1540
200 plus 280 is 480
and 2800 plus 280 3080

On Sunday, a local hamburger shop sold a combined total of 428 hamburgers and cheeseburgers. The number of cheese burgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Sunday?

Answers

The total number of hamburgerssold were 17.

What is equation modelling? What is a mathematical equation and expression?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.

A mathematical equation is used to equate two expressions.

Given is that on Sunday, a local hamburger shop sold a combined total of 428 hamburgers and cheeseburgers. The number of cheese burgers sold was three times the number of hamburgers sold.

Assume that the number of hamburgers sold are [x]. Then, the number of cheese burgers sold will be [3x]. Then, we can write -

x + 3x = 428

4x = 428

x = 17

Therefore, the total number of hamburgerssold were 17.

To solve more questions on equations, expressions and polynomials, visit the link below -

brainly.com/question/17421223

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The equation you can use is x + 3x = 428 with x as the number of cheeseburgers and 3x the number of hamburgers
you solve for x and get 4x= 428 and x=107

so 321 hamburgers were sold that day.

How can you solve -2y+5y=14

Answers

you add the terms that are the same and then simplify.

-2y+5y=3y
3y=14
y=4.666 or 4 2/3

The price of theater tickets was $50 two decades ago a report says that a ticket is 225% of what 20 years ago how much would it cost today?

Answers

225% of $50 is equal to 2.25*50
2.25*50 = 112.5

The ticket costs $ 112.50

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