
How do we find the latus rectum of the parabola .
Answer
414.3k+ views
Hint: We are given the equation of a parabola and we have to find the length of its latus rectum.
So, first, we will find the end coordinates of the latus rectum, and then using the distance formula, we will find its length.
General equation of parabola: , where, in the center of the parabola and is the focal length.
Distance between the points and is given by .
Complete step by step answer:
Given the equation of the parabola: .
To find the length of the latus rectum of the parabola.
Let the endpoints of the latus rectum of the parabola be and .
First, we will find these coordinates then their length.
Let , the coordinate is equivalent to . i.e., and since, is a point on the parabola, therefore, it satisfies the equation of a parabola, i.e., .
Taking square root, gives, .
Thus, the endpoints of the latus rectum of the parabola are and .
Now, the length of the latus rectum is given .
Putting values, we get, .
On solving, we get, length of the latus rectum .
Now, comparing the given equation with the general equation of a parabola, we get,
, as shown in the figure below,
Therefore, the length of the latus rectum of the parabola .
Note:In general, the length of the latus rectum of a parabola is , where, is the focal length.
In the conic section, the latus rectum is the chord drawn from the focus and is parallel to the directrix.
In general, there are 4 types of parabolas, with equations and .
So, first, we will find the end coordinates of the latus rectum, and then using the distance formula, we will find its length.
General equation of parabola:
Distance between the points
Complete step by step answer:
Given the equation of the parabola:
To find the length of the latus rectum of the parabola.
Let the endpoints of the latus rectum of the parabola be
First, we will find these coordinates then their length.
Let
Taking square root, gives,
Thus, the endpoints of the latus rectum of the parabola are
Now, the length of the latus rectum is given
Putting values, we get,
On solving, we get, length of the latus rectum
Now, comparing the given equation with the general equation of a parabola, we get,

Therefore, the length of the latus rectum of the parabola
Note:In general, the length of the latus rectum of a parabola is
In the conic section, the latus rectum is the chord drawn from the focus and is parallel to the directrix.
In general, there are 4 types of parabolas, with equations
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