Question

Find The equation for the ellipse that satisfies
The given compitions
Vertices (+5 o,) foci (+4, o)​

Answer 1

EXPLANATION.

Equation of ellipse that satisfied the given

conditions.

Vertices are = (+5,0).

Foci are = (+4,0).

Vertices are = (a, 0) Or (-a, 0).

Value of A = 5.

Foci are = (c, 0) Or (-c, 0).

Value of C = 4.

As we know that,

A² = B² + C²

(5)² = B² + (4)²

25 = B² + 16

B² = 25 - 16.

B² = 9

B = √9

B = 3.

General equation of ellipse

x²/a² + y²/b² = 1.

x²/(5)² + y²/(3)² = 1.

x²/25 + y²/9 = 1.

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

Find The equation for the ellipse that satisfies. The given compitions Vertices (+5 o,) foci (+4, o)

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{\pink{Given \: that}}}}$

• Vertices = ( + 5 , 0 ) $\large\purple{\texttt{Equation 1}}$
• Since, the vertices are of form = ( a + 0 ) $\large\purple{\texttt{Equation 2}}$

${\bigstar}\large{\boxed{\sf{\pink{To \: find}}}}$

• Equation for the ellipse.

${\bigstar}\large{\boxed{\sf{\pink{Solution}}}}$

Hence, the major axis is along x axis nd Equation of ellipse.

x² / a² + y² / b² = 1

$\large\red{\texttt{From equation 1 nd 2}}$

a = 5

Also given coordinate of foci = ( + 4 , 0 )

We know that $\large\purple{\texttt{Foci = +c , 0}}$

$\large\purple{\texttt{So, c = 4}}$

$\large\orange{\texttt{We know that}}$

➝ c² = a² - b²

➝ 4² = 5² - b²

➝ 16 = 25 - b²

➝ b² = 25 - 16

➝ b² = 9

➝ b = √9

$\large\green{\texttt{√ means square root}}$

$\large\green{\texttt{² means square}}$

➝ b = 3

{Result is 3 bcz √9 = 3 ( 3 × 3 = 9 )}

$\large{\boxed{\texttt{Hence, b = 3}}}$

Equation of ellipse is

$\frac{ {x}^{2} }{{a}^{2} } \: \: + \: \: \frac{ {y}^{2} }{ {b}^{2} } = 1$

$\large\purple{\texttt{Now putting value}}$

$\frac{ {x}^{2} }{ {5}^{2} } \: \: + \: \: \: \frac{ {y}^{2} }{ {3}^{2} } = 1$

$\frac{ { x }^{2} }{25} \: \: + \: \: \frac{ {y}^{2} }{9} = 1$

Hence, 1 is required answer.

@Itzbeautyqueen23

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