The area of 40x^2+45y^2=1800 is ------

Question

Not sure what is the area of

Answer 1

The equation is an ellipse. 

 

A = abπ, where a and b are the semi-axes.

 

40x²  + 45y² = 1800

40x²/1800 + 45y²/1800 = 1

x²/45 + y²/40 = 1

 

a = √45

a = 3√5

 

b = √40

b = 2√10

 

A = (3√5)(2√10)π

A = 6√50 π

A = 30√10 π

Answer 2

The equation can be simplified to (1/45)x² + (1/40)y² = 1

 

This can be thought of as a circle (x² + y² = 1) that is transformed into an ellipse. The circle of radius 1 is stretched by scale factor sqrt 45 units along the x axis and sqrt 40 units along the y axis, making it an ellipse. 

 

The area of a circle is given by  pi r² so the area of a unit circle is pi.

 

But the circle is stretched to an ellipse so the area  = (Pi) *(sqrt 45) * (sqrt 40)