Question

The graph of the equation x²= 4py is a parabola with focus F(_,_) and directrix y=_____ Therefore, the graph of x²=12y is a parabola with focus F(_,_) and a directrix y=_____

141

likes

703 views

Answer to a math question The graph of the equation x²= 4py is a parabola with focus F(_,_) and directrix y=_____ Therefore, the graph of x²=12y is a parabola with focus F(_,_) and a directrix y=_____

$Expert avatar$

Miles

4.9

114 Answers

The equation x² = 4py represents a parabola that opens upwards if p > 0 or downwards if p < 0. The focus of the parabola is at the point (0, p) and the directrix is the line y = -p. Therefore, for the equation x² = 12y, we can see that 4p = 12, so p = 3. This means the parabola opens upwards with the focus at the point F(0, 3) and the directrix at the line y = -3.

Frequently asked questions (FAQs)

What is the value of 3 to the power of 5, squared?

What is the missing side length when given two sides (a = 5, b = 7) and the included angle (θ = 60°) using the cosine law?

What is the equation of a hyperbola whose graph has a vertical transverse axis, center at (0,0), vertices at (0,3) and (0,-3), and foci at (0,5) and (0,-5)?

New questions in Mathematics

A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.

a ferry travels 1/6 of the distance between two ports in 3/7 hour. the ferry travels at a constant rate. at this rate, what fraction of the distance between the two ports can the ferry travel in one hour?

A person who weighs 200 pounds on earth would weigh about 32 pounds on the moon. Find the weight of a person on earth who would weigh 15 pounds on the moon.

Karina has a plot of 5,000 square meters in which she has decided that 60% of it will be used to plant vegetables. Of this part, 12% will be dedicated to planting lettuce. How much surface area of the plot will be used for cultivation?

I) Find the directional derivative of 𝑓(𝑥, 𝑦) = 𝑥 sin 𝑦 at (1,0) in the direction of the unit vector that make an angle of 𝜋/4 with positive 𝑥-axis.

Suppose the horses in a large stable, have a mean weight of a 807 pounds and a variance of 5776. What is the probability that the mean weight of the sample of horses with differ from the population mean by greater than 18 pounds is 41 horses are sampled at random from the stable round your answer to four decimal places.

Suppose SAT reading scores are normally distributed with a mean of 496 and a standard deviation of 109. The University plans towards scholarships for students who scores are in the top 7%. What is the minimum score required for the scholarship round your answer to the nearest whole number.

Log(45)

Suppose that you use 4.29 g of Iron in the chemical reaction: 2Fe(s) + 3 Cu2 + (aq) 2Fe 3 + (aq) + 3Cu(s ) - . What is the theoretical yield of Cu (s), in grams?

sum of 7a-4b+5c, -7a+4b-6c

In a 24 hours period, the average number of boats arriving at a port is 10. Assuming that boats arrive at a random rate that is the same for all subintervals of equal length (i.e. the probability of a boat arriving during a 1 hour period the same for every 1 hour period no matter what). Calculate the probability that more than 1 boat will arrive during a 1 hour period. (P(X>1) ) Give your answers to 4 decimal places and in a range between 0 and 1