Question

find the coordinates of the foci the vertices the length of major axis minor axis the eccentricity and the lenght of the of the latus rectum of the ellipes 25x2 + 49y2 = 1225

Answer 1

Answer:

Given equation is,

4x2+9y2=36

We will convert this equation into standard form.

⇒436x2+936y2=1

⇒x29+y24=1

So, this is our standard equation of ellipse with,

a=3,b=2

c=a2−b2−−−−−−√=9−4−−−−−√=5–√

Here, as a>b, major-axis will be X−axis.

Now, foci will be (±c,0)=(±5–√,0).

Vertices will be (±a,0)=(±3,0).

Length of major-axis =2a=6

Length of minor axis =2b=4

Eccentricity =ca=5–√3.

Length of latus rectum =2b2a=2∗43=83.