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 vertex form of a parabola given by the function 𝑦 = 2𝑥^2?
+
Question: Find the equation of a hyperbola with center (2, -3), vertices at (4, -3) and (0, -3), and a distance of 6 units from the center to the foci.
+
Question: What is the limit as x approaches 5 of (3x^2 + 2x - 7)?
+
New questions in Mathematics
1 + 1
-6n+5=-13
5(4x+3)=75
Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)
how many arrangement can be made of 4 letters chosen from the 8 letters of the world ABBSOLUTE
By direct proof, how can you prove that “The sum of any three consecutive even integers is always a multiple of 6”.
5.- From the probabilities: 𝐏(𝐁) = 𝟑𝟎% 𝐏(𝐀 ∩ 𝐁) = 𝟐𝟎% 𝐏(𝐀 ̅) = 𝟕𝟎% You are asked to calculate: 𝐏(𝐀 ∪ 𝐁)
If 0101, what is the binary representation of the 4x16 decoder output?
What is 28 marks out of 56 as a percentage
Two business partners have a bank balance of $17,942.00. After the first year their interest brings their balance to $18,928.91. What rate of interest is earned?
suppose random variable x follows poisson distribution with expected value 3. what is variance of x?
Calculate the value of a so that the vectors (2,2,−1),(3,4,2) and(a,2,3) are coplanar.
From 1975 through 2020 the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 34 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 800? Assume the standard deviation is 1539
effectiveness of fiscal and monetary policy under closed and open economies
A diamond ring was reduced from $999.99 to $689.99. Find the percent reduction in the price. Round the answer to the nearest tenth of a percent, if necessary.
Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)
What is the total amount due and the amount of interest on a 3-year loan of $1,000 at a simple interest rate of 12% per year?
22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.
5a-3.(a-7)=-3
f(x)= 9-x^2 find (f(x+h)-f(x) )/h