Table of Contents
How do you find the equation of a parabola with latus rectum?
use h, k, and p to find the coordinates of the focus, (h,k+p) use k and p to find the equation of the directrix, y=k−p. use h, k, and p to find the endpoints of the latus rectum, (h±2p,k+p)
How do you write latus rectum?
Latus Rectum of a Parabola The length of the latus rectum for a standard equation of a parabola y2 = 4ax is equal to LL’ = 4a. The endpoints of the latus rectum of a Parabola are (a, 2a), (a, -2a).
How do you find the opening of a parabola?
There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward. Study the graphs below: Figure \%: On the left, y = x2.
How do you find the equation of a parabola with the focus?
In order to find the focus of a parabola, you must know that the equation of a parabola in a vertex form is y=a(x−h)2+k where a represents the slope of the equation. From the formula, we can see that the coordinates for the focus of the parabola is (h, k+1/4a).
How do you find an equation of a parabola?
The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax.
How do you graph the latus rectum?
Find the length of the latus rectum whose parabola equation is given as, y2 = 12x. Hence, the length of the latus rectum of a parabola is = 4a = 4(3) =12….Solution:
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Which quadratic function opens downward?
The quadratic function f(x) = a(x – h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).
How to find the length of the latus rectum of a parabola?
Find the length of the latus rectum whose parabola equation is given as, y 2 = 12x. Since y 2 = 4ax is the equation of parabola, we get value of a: Hence, the length of the latus rectum of a parabola is = 4a = 4 (3) =12. Find the length of the latus rectum of an ellipse 4x 2 + 9y 2 – 24x + 36y – 72 = 0.
How do you find which side of a parabola opens?
Step 1 : Sketch the graph of the parabola using the given vertex and equation of latus rectum. Once the graph of the parabola is sketched, you can know to which side the parabola opens. Step 2 : Find the distance between vertex and focus to get the value of a. Step 3 :
What is the x coordinate of the vertex of the parabola?
The x coordinate of the vertex, h, is the midpoint between the x coordinates of the two points: We know that 4f is ± the length of the latus rectum: We are not told whether the parabola opens up or down and you have only asked for one of the two possible equations, therefore, I shall choose the positive value:
What is the equation for a parabola in the fourth quadrant?
Thus, the equation can be of the form x 2 = 4ay or x 2 = -4ay, where the sign depends on whether the parabola opens upwards or downwards. Since the parabola passes through (3, -4) which lies in the fourth quadrant, it must open downwards.