What would all values of a be so that this equation, X^2+3ax+y^2+4ay=0, has an area of 25pi/4? the radius is 5/2.
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completing the squares
x²+3ax+(3/2a)²+y²+4ay+(2a)²= +(3/2 a)²+(2a)²
(x+ 3/2 a)² +(y+2a)² = 9/4 a²+4a² =(9+16)/4 a² =R²
Area of the circle =
A=π R² =(25/4 a²
plug in value of R, solve for a
x²+3ax+(3/2a)²+y²+4ay+(2a)²= +(3/2 a)²+(2a)²
(x+ 3/2 a)² +(y+2a)² = 9/4 a²+4a² =(9+16)/4 a² =R²
Area of the circle =
A=π R² =(25/4 a²
plug in value of R, solve for a