A parabola is a plane curve formed by a point moving such that its distance from a fixed point is equal to its distance from a fixed-line. The fixed-line is the directrix of the parabola and the fixed point F is the focus. As far as JEE is concerned, parabola is an important topic in conics. In this article, we will learn how to find the equation of the parabola when latus rectum is given.
What is Latus Rectum of Parabola?
Latus Rectum is a line segment perpendicular to the axis of the parabola, through the focus and whose endpoints lie on the parabola.
The length of the latus rectum is given by 4a.
Standard Equation
The equation of the parabola with vertex at the origin, focus at (a,0) and directrix x = -a is
y2 = 4ax.
Solved Examples
Example 1
Find the equation of the parabola with latus rectum joining points (4, 6) and (4,-2).
Solution:
Given latus rectum joining the points (4, 6) and (4, -2).
So the length of latus rectum = √[(4-4)2 + (-2-6)2]
= √64
= 8
So 4a = 8
Equation of parabola is y2 = 4ax.
y2 = 8x is the required equation.
Example 2.
Find the equation of the parabola whose focus is at (3,0) and the length of the latus rectum is 12.
Solution:
Given length of latus rectum, 4a = 12
So a = 12/4 = 3
Equation of parabola is y2 = 4ax
y2 = 12x is the required equation.
Related Links:
JEE Important and Previous Year Questions on Parabola
Parabola
6 Important Problems on Parabola
Frequently Asked Questions
Give the standard equation of a Parabola.
The standard equation of the parabola with vertex at (0, 0), focus at (a, 0) and directrix x = -a is y2 = 4ax.
What is the length of the latus rectum of a Parabola?
The length of the latus rectum of a Parabola is given by 4a.
What do you mean by the latus rectum of a Parabola?
Latus Rectum is a line that is perpendicular to the axis of the parabola, through the focus and whose endpoints lie on the parabola.
How do you find the equation of a Parabola, if the latus rectum is given?
We find the value of ‘a’ from the latus rectum equation. Then substitute ‘a’ in the standard equation y2 = 4ax.
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