All categories

2 years ago

Match the steps to find the equation of the parabola with focus (-1,2) and directrix x=5

Mathematics

1 answer:

Paha777 [63]2 years ago

4 0

Given that parabola has a focus of (-1,2) and directrix of x=5, Matching the steps with the equations we shall have:
1. Use (x,y)⇒choose a point from the parabola.

2. √[(x+1)²+(y-2)²]⇒Find the distance from the focus to the point on the parabola

3. √(x-5)²⇒Find the distance from the point on the parabola to the directrix

4. √[(x+1)²+(y-2)²]=√(x-5)²⇒Set the distance from focus to the point equal to the distance from directrix to the point

5. (x+2)²+(y-2)²=(x-5)² ⇒Square both sides and simplify
y²-4y+4=-12x+24

6. x=-y²/12+y/3+5/3⇒Write the equation of the parabola

You might be interested in

Please help find the anwser to question 1 and 2

grin007 [14]

16ft and 25ft sorry if i’m wrong

4 0

2 years ago

One endpoint of a line segment is (–6, 4), and the midpoint of the segment is (–2, 7). What are the coordinates of the other end

Arturiano [62]

Answer:

A. (2, 10)

Step-by-step explanation:

If there are two points (x1,y1) and (x2,y2) on a coordinates plane then

coordinates of the midpoint is given by (x1+x2)/2, (y1+y2)/2

__________________________________________________

Given

one endpoint is (–6, 4) and midpoint is (–2, 7)

let coordinates of other endpoint be (x,y)

now if one endpoint is (–6, 4) and other endpoint is (x,y)

then coordinates of midpoint is ((-6+x)/2 , (4+y)/2)

while the coordinates of midpoint given is (–2, 7)

thus (–2, 7) should be equal to ((-6+x)/2 , (4+y)/2)

-2 = (-6+x)/2 and 7 = (4+y)/2

=> -2*2 = -6+x => 7*2 = 4+y

=> -4 = -6+x => 14 = 4+y

=> -4+6 = x => 14-4 = y

=> x = 2 => 10 = y

Thus, coordinates of the other endpoint is(2,10)

6 0

2 years ago

Evaluate the expression. 5 x (-6 / -1 + -10)

kotykmax [81]

Answer:

-20

Step-by-step explanation:

$5 * (-6 / -1+ -10)$

According to PEMDAS, we need to do the math in the parentheses first.

$-6 / -1 + -10$

Applying PEMDAS to the inside of the parentheses, then we have to divide -6 by -1, where we would get 6.

$6 + -10$

Adding a negative is the same as subtracting, so adding negative 10 is the same as subtracting 10.

$6 - 10$

Subtracting, we get 6 - 10 = -4 and we're left with:

$5 * (-4)$

Multiplying, <u>our final answer is -20.</u>

Hope this helps!

8 0

1 year ago

Bosade wala iuftiurtioiuuu8ii

stepan [7]

Answer:

hi :)

Step-by-step explanation:

7 0

2 years ago

Will has 20 pounds of apples he makes to back to apple sauce that he's 4 pounds each one back to apple butter that use a 6 pound

Ulleksa [173]

Answer:

The equation representing pounds of apples will has left $x=20-4-6-3$ .

Will has left with 7 pounds of apples.

Step-by-step explanation:

Given:

Total pounds of apple = 20 pounds.

Pounds of apple used for apple sauce = 4 pounds

Pounds of apple used for apple butter = 6 pounds

Pounds of apple used for making juice = 3 pounds

We need to write the equation to represent pounds of apples will has left.

Solution:

Let us assume pounds of apples will has left be 'x'.

So we can say that;

pounds of apples will has left can be calculated by subtracting Pounds of apple used for apple sauce and Pounds of apple used for apple butter and Pounds of apple used for making juice from Total pounds of apple.

framing in equation form we get;

$x=20-4-6-3$

Hence The equation representing pounds of apples will has left $x=20-4-6-3$ .

On Solving the above equation we get;

$x=7\ pounds$

Hence Will has left with 7 pounds of apples.

4 0

2 years ago