Area Inside Circle x^2+y^2=a^2 Above b=7

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In summary, the conversation discusses finding the area inside a circle above a given line, with a range for the line's y-value. The conversation also briefly touches on using integrals and a geometric method to find the area.
  • #1
wonguyen1995
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Find area inside circle x^2+y^2=a^2, above 7=b, -a \le b \le a ?? i think f of y right?
(-a to a) minus (-a to b)?
 
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  • #2
wonguyen1995 said:
Find area inside circle x^2+y^2=a^2, above 7=b, -a \le b \le a
Maybe it's a typo and should read "above $y=b$". That is, find the area inside the circle $x^2+y^2=a^2$ that is located above the line $y=b$, where $-a\le b\le a$.

wonguyen1995 said:
?? i think f of y right?
(-a to a) minus (-a to b)?
Sorry, I don't understand your remark.
 
  • #3
Evgeny.Makarov said:
Maybe it's a typo and should read "above $y=b$". That is, find the area inside the circle $x^2+y^2=a^2$ that is located above the line $y=b$, where $-a\le b\le a$.

Sorry, I don't understand your remark.

That is it, i mistake.
so can you help me??
 
  • #4
Do you need a solution that uses integral? It's easier to find the area geometrically as described in Wikipedia using the fact that the area of a triangle with sides $u$ and $v$ and angle $\varphi$ between them is $\frac{1}{2}uv\sin\varphi$.
 

FAQ: Area Inside Circle x^2+y^2=a^2 Above b=7

What is the formula for finding the area inside a circle?

The formula for finding the area inside a circle is A = πr^2, where A is the area and r is the radius.

How does the variable 'b' affect the area inside a circle with equation x^2+y^2=a^2 above b=7?

The variable 'b' in this equation represents the y-coordinate of the point where the circle intersects the x-axis. The area inside the circle above b=7 would be the portion of the circle that lies above the line y=7. This would result in a smaller area compared to the full circle with radius a.

Can the area inside a circle be negative?

No, the area inside a circle cannot be negative. It is always a positive value, as it represents the amount of space enclosed by the circle.

How does the value of 'a' affect the area inside a circle with equation x^2+y^2=a^2 above b=7?

The value of 'a' represents the radius of the circle. As 'a' increases, the area of the circle also increases. However, in the case of x^2+y^2=a^2 above b=7, the value of 'a' does not have a direct effect on the area above b=7, as it only affects the size of the entire circle.

Is the area inside a circle above b=7 always the same for different values of 'a'?

No, the area inside a circle above b=7 will vary depending on the value of 'a'. As 'a' increases, the area of the circle increases, but the area above b=7 remains the same. However, if 'a' is kept constant, the area above b=7 will also be constant as long as the circle intersects the x-axis at y=7.

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