How do you find the parabola with 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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How do you find the equation of a parabola whose focus and Directrix is given?
Let (x0,y0) be any point on the parabola. Find the distance between (x0,y0) and the focus. Then find the distance between (x0,y0) and directrix. Equate these two distance equations and the simplified equation in x0 and y0 is equation of the parabola.
What is the equation of Directrix of parabola?
The axis of the parabola is y-axis. Equation of directrix is y = -a. i.e. y = -½ is the equation of directrix. Vertex of the parabola is (0,0).
How do you find the Directrix of latus rectum?
use h, k, and p to find the coordinates of the focus, (h+p,k) use h andp p to find the equation of the directrix, x=h−p. use h, k, and p to find the endpoints of the latus rectum, (h+p,k±2p)
Is latus rectum always 4a?
Latus rectum of parabola formula is 4a, where a is the distance of the focus from the vertex of the parabola.
Which equation represents the Directrix?
Which equation represents the directrix? A parabola has a vertex at (0,0). The equation for the directrix of the parabola is x = -4.
Is the Directrix perpendicular to the latus rectum?
See Figure 3. Notice that the axis of symmetry passes through the focus and vertex and is perpendicular to the directrix. The vertex is the midpoint between the directrix and the focus. The line segment that passes through the focus and is parallel to the directrix is called the latus rectum.
Is latus rectum Directrix?
A parabola is the set of all points (x,y) in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix. The line segment that passes through the focus and is parallel to the directrix is called the latus rectum.
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 to find the directrix and focus of a parabola?
Focus of the parabola is (a, 0) = (3, 0). Equation of the directrix is x = -a, i.e. x = -3 or x + 3 = 0. Example 2: Find the equation of the parabola which is symmetric about the y-axis, and passes through the point (3, -4). Given that the parabola is symmetric about the y-axis and has its vertex at the origin.
What is the formula to find the direction of parabola?
Parabola Formula 1 The direction of the parabola is determined by the value of a. 2 Vertex = (h,k), where h = -b/2a and k = f (h) 3 Latus Rectum = 4a 4 Focus: (h, k+ (1/4a)) 5 Directrix: y = k – 1/4a More
What is the vertex of a parabola?
Also, the vertex is the point of intersection of a parabola with the axis. As we know, the standard equation of the parabola is used in solving a variety of problems in maths.