All categories

3 years ago

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

Mathematics

1 answer:

Likurg_2 [28]3 years ago

5 0

Answer:

Step-by-step explanation:

The correct option is option (C).

The required equation of the parabola is

Step-by-step explanation:

Formula:

The distance of a point (x₁,y₁) from a line ax+by+c=0 is

The distance between two points (x₁,y₁) and (x₂,y₂) is

Given that, the focus of the parabola is (2,3) and directrix y= - 1.

We know that, a parabola is the locus of points that equidistant from the directrix and the focus.

Let any point on the parabola be P(x,y) .

The distance of P from the directrix is

=y+1

The distance of the point P from the focus (2,3) is

According to the problem,

The required equation of the parabola is

You might be interested in

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total

IrinaK [193]

200 x 5 = 1000
1210 x 3 = 3630
3630 + 1000 = 4630

She bought 5 coach tickets and 3 first class.

3 0

2 years ago

Read 2 more answers

Which equation relates the number of triangles in the figure (n) to the perimeter of the figure (p)

WITCHER [35]

Answer:

Option d is correct.

Equation : P=7n+20.

Explanation;

Given the perimeter of each figure is;

Perimeter of triangle is equal to the sum of all the sides of a triangle.

Perimeter of 1 triangle is 21

Perimeter of 2 triangle is 34 and

Perimeter of 3 triangle is 41

Let n be the number of figure and P be the perimeter of the figure;

the only equation which satisfy the given perimeter is;

$P=7n+20$

Check:

for n =1 which means 1 triangle then;

$P =7n+20 = 7 \cdot 1 +20 = 7+20 = 27$

for n = 2 , [ i.e 2 triangle]

$P =7n+20 = 7 \cdot 2 +20 = 14+20 = 34$

and for n =3 [i.e, 3 triangles]

$P =7n+20 = 7 \cdot 3 +20 = 21+20 = 41$

Therefore, the equation P =7n+20 relates the number of triangles in the figure(n) to the perimeter of the figure(P).

3 0

3 years ago

Margie has 5 times as many nickels as quarters. She has a total of $2.00.

stich3 [128]

Answer:

Part A:

n = 5q (1st equation)

0.05n + 0.25q = 2 (2nd equation)

Part B:

q = 4 ⇒ n = 5 * 4 = 20

Part C:

Margie has 20 nickels and 4 quarters, for a total of $ 2.00

Step-by-step explanation:

Let's recall that a nickel has a value of $ 0.05 and a quarter a value of $ 0.25.

Let n represent the number of nickels and q represent the number of quarters.

Part A:

Write a system of equations to represent the situation.

n = 5q (1st equation)

n * 0.05 + q * 0.25 = 2

0.05n + 0.25q = 2 (2nd equation)

Part B:

Replacing n in the 2nd equation to solve for q:

0.05n + 0.25q = 2

0.05 * 5q + 0.25q = 2

0.25q + 0.25q = 2

0.5q = 2

q = 2/0.5

q = 4 ⇒ n = 5 * 4 = 20

Part C:

Margie has 20 nickels and 4 quarters, for a total of $ 2.00

3 0

3 years ago

Can y’all please help me? :,)

Step2247 [10]

Answer:

sorry but i cant answer that quiestion

7 0

3 years ago

During his speech at the Creating Digital Dividends Conference in October 2000, Bill Gates said, "I’m a great believer that any

natali 33 [55]

Answer:

Step-by-step explanation:

If you look at it this way, one can say that algebra does act as a tool to improve communication in the sense that, it is similar, in a way, to learning a new language. You don't rush into it, you start rather gently, little by little, step by step before you can say, you fully get it. We can then agree that this will improve one's communication prowess because the person would be learning something new with the help of some other people.

3 0

3 years ago