R = - mQ2 + nQ ( m,n > 0)
C = aQ2 + bQ + c (a,b,c > 0)
Suppose that the government plans to levy an excise tax on the product of this firm and
wishes to maximise the total tax revenue T from this source. What tax rate t ( rupees per
unit of output) should the government choose?
Answers
Answer:
Answer:
Given :-
\longmapsto \sf x^2 + y^2 + 4x + 8y + 11 =\: 0⟼x
2
+y
2
+4x+8y+11=0
To Find :-
What is the center and radius.
Solution :-
First, we have to find the radius of the circle :
Given equation :
\mapsto \sf x^2 + y^2 + 4x + 8y + 11 =\: 0↦x
2
+y
2
+4x+8y+11=0
Now, as we know that :
\clubsuit♣ The general equation of a circle :
{\small{\bold{\purple{\underline{\leadsto\: x^2 + y^2 + 2gx + 2fy + c =\: 0}}}}}
⇝x
2
+y
2
+2gx+2fy+c=0
Then,
g = 2
f = 4
c = 11
Now, by putting the values we get,
\implies \sf x^2 + y^2 + 2(2)x + 2(4)y + 11 =\: 0⟹x
2
+y
2
+2(2)x+2(4)y+11=0
Now, as we know that :
\begin{gathered} \longmapsto \sf\boxed{\bold{\pink{Radius\: (R) =\: \sqrt{{(g)}^{2} + {(f)}^{2} - c}}}}\\\end{gathered}
⟼
Radius(R)=
(g)
2
+(f)
2
−c
Given :
g = 2
f = 4
c = 11
According to the question by using the formula we get,
\implies \sf Radius\: (R) =\: \sqrt{{(2)}^{2} + {(4)}^{2} - 11}⟹Radius(R)=
(2)
2
+(4)
2
−11
\implies \sf Radius\: (R) =\: \sqrt{2 \times 2 + 4 \times 4 - 11}⟹Radius(R)=
2×2+4×4−11
\implies \sf Radius\: (R) =\: \sqrt{4 + 16 - 11}⟹Radius(R)=
4+16−11
\implies \sf Radius\: (R) =\: \sqrt{20 - 11}⟹Radius(R)=
20−11
\implies \sf Radius\: (R) =\: \sqrt{9}⟹Radius(R)=
9
\implies \sf\bold{\red{Radius\: (R) =\: 3}}⟹Radius(R)=3
\therefore∴ The radius of the circle is 3 .
\rule{150}{2}
Now, we have to find the center of the circle :
As we know that :
\longmapsto \sf\boxed{\bold{\pink{Center =\: - g , - f}}}⟼
Center=−g,−f
Given :
g = 2
f = 4
Then,
\implies \sf Center =\: - 2 , - 4⟹Center=−2,−4
\implies \sf\bold{\red{Center =\: - 2 , - 4}}⟹Center=−2,−4
\therefore∴ The center of the circle is - 2 , - 4 .