Dada la ecuacion 25x2 + 4y2 = 100, determina las coordenadas de los vertices, focos, las longitudes de los respectivos ejes mayor y menor, la excentricidad, la longitud de los lados rectos y realiza la representacion grafica

URGENTE

The given equation is

Which represents an elipse.

To find its elements, we need to divide the equation by 100

Where and . Remember that the greatest denominator is , and the least is . So, we extract the square root on each equation.

and .

In a elipse, we have a major axis and a minor axis. In this case, the major axis is vertical and the minor axis is horizontal, that means this is a vertical elipse.

The length of the major axis is .

The length of the minor axis is .

The vertices are and .

Now, the main parameters of an elipse are related by

, which we are gonna use to find , the parameter of the focus.

So, the coordinates of each focus are and

The eccentricity of a elipse is defined

The latus rectum is defined

Finally, the graph of the elipse is attached.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.