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How do you find the equation of a parabola given the latus rectum?

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How do you find the equation of a parabola given the latus rectum?

Given latus rectum joining the points (4, 6) and (4, -2). Equation of parabola is y2 = 4ax. y2 = 8x is the required equation.

How do you measure the length of a latus rectum?

Thus, the length of the latus rectum of a parabola is 4a= 4(3) = 12….Latus Rectum of Conic Section Introduction

  1. Latus rectum is always equivalent to the length of the diameter in a circle.
  2. The length of the latus rectum in a parabola is equal to the four times the focal length.

How do you find the vertex?

We find the vertex of a quadratic equation with the following steps:

  1. Get the equation in the form y = ax2 + bx + c.
  2. Calculate -b / 2a. This is the x-coordinate of the vertex.
  3. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.
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What is the length of latus rectum If the length of the axis of symmetry from focus to Directrix is 5 units?

Hence, length of latus rectum is 10 .

How do you find the length of the latus rectum ellipse?

Latus Rectum of Ellipse Latus rectum of the ellipse is defined as the length of the line segment perpendicular to the major axis passing through any of the foci and whose endpoint lies on the ellipse. The length of the latus rectum of an ellipse is 2b²/ a.

How do you find the vertex and axis of symmetry?

The Vertex Form of a quadratic function is given by: f(x)=a(x−h)2+k , where (h,k) is the Vertex of the parabola. x=h is the axis of symmetry.

How do you solve for vertex form?

How to find a parabola’s equation using its Vertex Form

  1. Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola’s equation in the form: y=a(x−h)2+k.
  2. Step 2: find the value of the coefficient a by substituting the coordinates of point P into the equation written in step 1 and solving for a.
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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 length of the latus rectum of conic sections?

The summary for the latus rectum of all the conic sections are given below: Conic Section. Length of the Latus Rectum. Ends of the Latus Rectum. y 2 = 4ax. 4a. L = (a, 2a), L’ = (a, -2a) (x 2. /a 2) + (y 2. /b 2) =1. If a>b; 2b 2 /a.

What is the meaning of latus rectum?

The word latus rectum is derived from the Latin word “latus” which means “side”, and the “rectum” which means “straight”. Half the latus rectum is called the semi latus rectum. The diagram above shows the latus rectum of a parabola.

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How do you find the directrix and vertex of a parabola?

How to find the directrix, focus and vertex of a parabola y = ½ x 2. 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). Put your understanding of this concept to test by answering a few MCQs.