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=_____

Name: Solved: 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=_____ - MathMaster
Brand: MathMaster
Rating: 4.9 (141 reviews)

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)

Which sign of equality represents congruent triangles?

What is the derivative of f(x) = 3x^2 + e^x - ln(x)?

What is the length of the hypotenuse if the adjacent side measures 5 units and the opposite side measures 12 units?

New questions in Mathematics

Add. 7/w²+18w+81 + 1/w²-81

CASE 6-1: PREPARE A PRODUCTION PLAN: WHAT PROBLEMS ARRIVE? Midwest Plastics Company has conducted profit planning for several years. The president stated (with justification) that inventory control and planning had not been satisfactory, which was mainly due to poor planning of production and inventory budgets. Please analyze and provide recommendations, in detail, on the issue regarding the 20B profit plan, which is now being prepared. Their analysis and recommendations will be presented to the executive committee. Despite the seasonality factor, the sales department has been successful in developing a sales plan, on a monthly basis, for each year. The following sales data is available for 20B. 1. Sales plan summary for 20B: 2. Finished goods inventory, as of January 1, 20B, is 96,000 units. 3. Work-in-process inventory will remain constant. 4. Actual annual sales in 20A, including the estimate for December, were 350,000 units. 5. The average finished goods inventory during 20A was 70,000 units. IT IS REQUESTED. 1. Prepare the annual production budget, assuming that management policy is to budget ending finished goods inventory at a standard quantity, based on the ratio of historical sales of 20A to inventory turnover. 2. Prepare a schedule showing sales, production, and inventory levels for each month, assuming: 1) stable inventory, 2) stable production, and 3) recommended inventory-production levels. In developing your recommendations, assume that the following policies have been established: a) The president has set the policy that a maximum inventory of 85,000 units and a minimum inventory of 75,000 units should be used, except in abnormal circumstances. b) A stable level of production is definitely preferred, except that during the holiday season in July and August, production may be reduced by 25 percent. Likewise, a variation in production of 7.5 percent above and below the average level is acceptable. 3. What are the main problems faced by the company in production planning? Make your general recommendations.

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=_____

The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March are listed below. 23.0 21.2 23.5 23.6 20.1 24.3 25.2 26.9 24.6 22.6 26.1 23.1 25.8 24.6 24.3 24.1 24.8 22.1 22.8 24.5 (a) Find the z-scores for the largest measurement. (Round your answers to two decimal places.) z =

The average number of babies born at a hospital is 6 per hour. What is the probability that three babies are born during a particular 1 hour period?

Determine the reduced equation of the straight line that is perpendicular to the straight line r: y=4x-10 and passes through the origin of the Cartesian plane

Calculate the boiling temperature and freezing temperature at 1 atmosphere pressure of a solution formed by dissolving 123 grams of ferrous oxide in 1.890 grams of HCl.