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The area (in sq. units) of the region enclosed by the ellipse 16x2+25y2=40016x^2 + 25y^2 = 400 is

Solution

✅ Correct Option: 4

The ellipse equation is 16x2+25y2=40016x^2 + 25y^2 = 400.

The standard form of an ellipse is x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.

Dividing the entire equation by 400:

16x2400+25y2400=400400\frac{16x^2}{400} + \frac{25y^2}{400} = \frac{400}{400}

x225+y216=1\frac{x^2}{25} + \frac{y^2}{16} = 1


From x225+y216=1\frac{x^2}{25} + \frac{y^2}{16} = 1:

a2=25a^2 = 25

a=5a = 5

b2=16b^2 = 16

b=4b = 4


The area of an ellipse is given by πab\pi ab.

Area =π×5×4= \pi \times 5 \times 4

Area =20π= 20\pi sq. units

Therefore, the area of the region enclosed by the ellipse is 20π20\pi square units.

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