All categories

3 years ago

What is the equation of the parabola with focus (4,1) and directrix y= 2?

Mathematics

1 answer:

mariarad [96]3 years ago

8 0

It’s A I think I had it on a recent test :) I’m not sure tho

You might be interested in

I need the answer for this exact question

denis23 [38]

Answer:

$y=\frac{7}{2}x-20$

Step-by-step explanation:

Let the equation of the line be $y-y_1=m(x-x_1)$ where, 'm' is its slope and $(x_1,y_1)$ is a point on it.

Given:

The equation of a known line is:

$y=-\frac{2}{7}x+9$

A point on the unknown line is:

$(x_1,y_1)=(4,-6)$

Both the lines are perpendicular to each other.

Now, the slope of the known line is given by the coefficient of 'x'. Therefore, the slope of the known line is $m_1=-\frac{2}{7}$

When two lines are perpendicular, the product of their slopes is equal to -1.

Therefore,

$m\cdot m_1=-1\\m=-\frac{1}{m_1}\\m=-\frac{1}{\frac{-2}{7} }=\frac{7}{2}$

Therefore, the equation of the unknown line is determined by plugging in all the given values. This gives,

$y-(-6))=\frac{7}{2}(x-4)\\y+6=\frac{7}{2}x-14\\y=\frac{7}{2}x-14-6\\\\y=\frac{7}{2}x-20$

The equation of a line perpendicular to the given line and passing through (4, -6) is $y=\frac{7}{2}x-20$ .

3 0

3 years ago

(a - b)(a2 + ab + b2)

Colt1911 [192]

Answer:

THE ANSWER IS THIS FOR THE QUESTION UP TOP

8 0

3 years ago

Which of the following is not a property of mathematical proofs?

Contact [7]

There are no properties of mathematical proofs
on the list of choices that you have offered.

7 0

3 years ago

Find the slope and y-intercept for this table.

labwork [276]

Answer:

See below:

Step-by-step explanation:

To find the slope, we use the following formula:

$\frac{y_{2} - y_{1} }{x_{2} - x_{1} }$

For this case, we can use (6,60) as the first set of points.

We can use (4,70) as the second set of points.

Now, we can use the formula, 70-60 is for the top of the fraction (10)

We can do 4-6 to find the bottom, which is (-2)

Now, if we add the fraction back we get -> 10/-2 which is -5 for slope!

To find out the y intercept, it in simple words is "What is y when x is 0?".

We can do that by using the slope intercept formula: $y=mx+b$ .

Once we insert our slope which is -2 we get: $y=-2x+b$

We can now substitute a point, lets use (6,60) so we can find out b.

We now get the equation: $60=-5(6)+b$ .

If we solve for that we get 90!

Once we input that, we get, $y=-5x+90$

Now we put in x as 0 and we get our y intercept as 90!

If this answer helped, consider marking as brainliest!!

8 0

3 years ago

Valentina's family is planning to have a party for her quinceanera. They are considering two different locations to rent for her

CaHeK987 [17]

Answer:

number of hours = 3 hours

Step-by-step explanation:

Let

x = number of hours

Casa Lucia = 200 + 500x

Silver Fox = 1,100 + 200x

To solve the equation, equate both cost of rent

Casa Lucia = Silver Fox

200 + 500x = 1,100 + 200x

200 - 1,100 = 200x - 500x

-900 = - 300x

x = -900 / -300

x = 3 hours

number of hours = 3 hours

The solution to the system of equations in this real-world context represents the number of hours both locations can be rented with the same cost.

It means both locations cost the same if rented for 3 hours each

3 0

3 years ago