$MathMaster logo$

MathMaster

Home
general
the graph of the equation x 4py is a parabola with focus f and directrix y therefore the graph of x 12y is a parabola with

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=_____

$Expert avatar$

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)

Math question: Simplify log(6a) - log(a^2) - log(18) using logarithmic properties

+

Math question: What is the limit as x approaches infinity of (2x^3 + 3x^2 + 5)/(x^3 - 4x^2 + 2x + 7)?

+

Math Question: "If log base 5 of x equals 3, then what is the value of x?"

+

New questions in Mathematics

Calculate to represent the function whose graph is a line that passes through the points (1,2) and (−3,4). What is your slope?

90 divided by 40

The profit G of the company CHUNCHES SA is given by G(x) = 3×(40 – ×), where × is the quantity of items sold. Find the maximum profit.

Which of the following is the product of multiplying twenty-seven and twenty-five hundredths by nine and twenty-seven hundredths?

In a normally distributed data set a mean of 31 where 95% of the data fall between 27.4 and 34.6, what would be the standard deviation of that data set?

Estimate the fifth term if the first term is 8 and the common ratio is -1/2

In the telephone exchange of a certain university, calls come in at a rate of 5 every 2 minutes. Assuming a Poisson distribution, the average number of calls per second is: a) 1/8 b) 1/12 c) 1/10 d) 2/5 e) 1/24

A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 60% of the people get vaccinated. If a person is selected at random from this region, find the probability that he or she will contract the disease. (4 Points)

A researcher is interested in voting preferences on change of the governing constitution in a certain country controlled by two main parties A and B. A questionnaire was developed and sent to a random sample of voters. The cross tabs are as follows Favour Neutral Oppose Membership: Party A 70 90 85 Party B 50 50 155 Test at α = 0.05 whether party membership and voting preference are associated and state the conditions required for chi-square test results to be valid.

cube root of 56

A person runs 175 yards per minute write a variable that represents the relationship between time and distance

Find the vertex F(x)=x^2-10x

A psychologist is investigating the levels of test anxiety in various university courses. Anxiety is measured on a scale ranging from 0 to 100, where 0 indicates the complete absence of anxiety and 100 represents an extreme level of anxiety. From the data obtained, it has been discovered that the psychology score is triple that of nursing, and in turn, the latter has a score 10 points lower than the nutrition major. Furthermore, the score in the veterinary degree is 15 points higher than that of nutrition. Finally, if we add the scores of all the races, we will obtain a total of 173 points. Pose the equation that represents the situation described in the previous problem and determine: What is the score that psychology obtained regarding its anxiety level before the exams?

Find I (Intrest) using simple interest formula of 17700 @ 15% for 4 years

If the area of a circle is 75.7ft2, what is the radius? Give the answer in metres. Round answer to 2 decimal places and enter the units.

Matilde knows that, when driving her car from her office to her apartment, she spends a normal time of x minutes. In the last week, you have noticed that when driving at 50 mph (miles per hour), you arrive home 4 minutes earlier than normal, and when driving at 40 mph, you arrive home 5 minutes earlier later than normal. If the distance between your office and your apartment is y miles, calculate x + y.