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Solution :

Given equation is,<br>
`16x^2+y^2 = 16`<br>
We will convert this equation into standard form.<br>
`=>16/16x^2+1/16y^2 = 1`<br>
`=> x^2/1+y^2/16 =1 `<br>
So, this is our standard equation of ellipse with, <br>
`a = 1, b = 4`<br>
`c = sqrt(b^2-a^2) = sqrt(16-1) = sqrt15`<br>
Here, as `b gt a`, major-axis will be `Y-`axis.<br>
Now, foci will be `(0,+-c) = (0,+-sqrt15).`<br>
Vertices will be `(0,+-b) = (0,+-4).`<br>
Length of major-axis ` = 2b = 8`<br>
Length of minor axis ` = 2a = 2`<br>
Eccentricity `= c/b = sqrt15/4.` <br>
Length of latus rectum ` = 2a^2/b = 2**1/4 = 1/2.`
**Ellipse Introduction**

**Equation of ellipse in its standard equation**

**Various result of Ellipse :- Vertices; major and minor axis ; focii directrix and center**

**Various results of ellipse when y-axis is major axis**

**Equation of an ellipse whose axes are parallel to co-ordinate axes and center is `(h,k)`**

**Some important terms of ellipse :- Ordinate; Double ordinate ;latus rectum.**

** Position of a point with respect to ellipse **

**Ellipse with axis not parallel to coordinate axis**

**Relation between all the terms of ellipse and major- minor axis when axis is not parallel to co ordinate axes**

** Auxiliary circle and eccentric angle**