Question

area enclosed within the ellipse 5x^2 + 2y^2 =80 is ???​

Answer 1

GIVEN :

Ellipse 5x² + 2y² =80

TO FIND :

Area enclosed within the given ellipse 5x² + 2y²=80

FORMULA USED:

Area of ellipse(A) :-

$A = \pi \: ab$

where ellipse standard Equation :-

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

where ,

• a= major axis
• b = minor axis

SOLUTION:

Given equation of ellipse :- 5x² + 2y²=80

Now ,

$⟹ \frac{5x²}{80} + \frac{ 2y²}{80} =1$

$⟹\frac{x²}{16} + \frac{ y²}{40} =1$

⟹ therefore , a² = 16

⟹ a = 4

⟹ b² = 40

⟹ b = √40

area of ellipse(A) = π ab

⟹ A = π × 4 × √40 square unit

⟹ A = 8√10 × 3.14 square unit

⟹ A = 25.12√10 square unit

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Learn more :-

Area of circle = π (radius)²

Area of rectangle = length × breadth

Area of square = (Side)²

Area of triangle = 1/2 × base × height

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Answer 2

Given :   5x^2 + 2y^2 =80

To Find : area enclosed within the ellipse

Solution:

5x² + 2y² =80

Dividing bith sides by 80

x²/16 + y²/40  = 1

=> x²/4²  + y²/(2√10)² = 1

Comparing with

x²/a² + y²/b² = 1

=> a = 4

& b = 2√10

Area enclosed within the ellipse = π ab

= π (4)(2√10)

= 79.4  sq units

Area enclosed within the ellipse   5x² + 2y² =80   is  79.5  sq units

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