Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x axis.

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Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x axis.

Given:

$b\text{ }=\text{ }3,\text{ }c\text{ }=\text{ }4,$

focus at the beginning and foci on the $x-axis$ .

Since the foci are on the $x-axis$ , the significant hub is along the $x-axis$ .

In this way, the condition of the ellipse will be of the structure

${{x}^{2}}/{{a}^{2}}~+\text{ }{{y}^{2}}/{{b}^{2}}~=\text{ }1$

, where ‘ $a$ ‘ is the semi-significant pivot.

Then, at that point,

$b\text{ }=\text{ }3\text{ }and\text{ }c\text{ }=\text{ }4.$

It is realized that

${{a}^{2}}~=\text{ }{{b}^{2~}}+\text{ }{{c}^{2}}.$

${{a}^{2}}~=\text{ }{{3}^{2~}}+\text{ }{{4}^{2}}$

$=\text{ }9\text{ }+\text{ }16$

$=25$

$a\text{ }=\text{ }\surd 25$

$=\text{ }5$

∴ The condition of the ellipse is

${{x}^{2}}/{{5}^{2}}~+\text{ }{{y}^{2}}/{{3}^{2}}~or\text{ }{{x}^{2}}/25\text{ }+\text{ }{{y}^{2}}/9\text{ }=\text{ }1$

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