How do you simplify a circle equation?

We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.

What is the general form equation of a circle?

Standard form for the equation of a circle is (x−h)2+(y−k)2=r2. The center is (h,k) and the radius measures r units. To graph a circle mark points r units up, down, left, and right from the center.

How do you find the equation of a circle?

To find the equation of a circle when you know the radius and centre, use the formula ( x − a ) 2 + ( y − b ) 2 = r 2 , where represents the centre of the circle, and is the radius. This equation is the same as the general equation of a circle, it's just written in a different form.

How do you find the center of a circle given an equation?

If the equation of a circle is given, then we can find its radius and center by comparing it with the general form of the equation: (x - h)² + (y - k)² = r². We will find the values of h, k, and r. Then, (h, k) will be the coordinates of the center of circle and r will be the radius.

How do you solve for radius and diameter?

How to find the center and radius of a circle in standard form

How do you calculate area of a circle?

The area of a circle is pi times the radius squared (A = π r²).

Why is the equation of a circle?

So set a = h and b = k in the formula, and because we know that the distance must be r, we can also replace d by r. Finally, if you square both sides of this equation, you end up with exactly the equation of a circle!

How do you find the area and circumference of a circle?

To find the circumference, you double the radius and multiply by pi. To find the area, you square the radius and multiply by pi.

How do you find the area with the radius?

To find the area using the radius, or the length from the center of the circle to the edge, use the formula area = πr^2, where r is the radius. For example, if the radius of the circle is 6 inches, first you would square 6 and get 36. Then, you would multiply 36 by π and get 113.04.

How do you find the radius with the diameter and circumference?

The circumference of a circle is equal to pi times the diameter. The diameter is two times the radius, so the equation for the circumference of a circle using the radius is two times pi times the radius.

How did you find the center and radius of the circle given its equation?

In order to find the center and radius, we need to change the equation of the circle into standard form, ( x − h ) 2 + ( y − k ) 2 = r 2 (x-h)^2+(y-k)^2=r^2 (x−h)2​+(y−k)2​=r2​, where h and k are the coordinates of the center and r is the radius.

How do you convert area to circumference?

The formula C = 2√πA is designed to find a circle's circumference using the area (A). Alternatively, you can solve the equation A = πR² in reverse to find R, then plug R into the circumference equation. Both equations provide the same result.

What is the area of the sector if the diameter is 12 cm and the angle is 60?

∴ The area of sector is 75. 36 cm2.

How do you find the area of a sector of a circle without angle?

How to Find the Area of a Sector Without Angle? If the sector angle is not given, but we know the arc length and the radius, the area of a sector can be calculated. We first find the sector angle by substituting the given values of the arc length and radius in the formula, Length of Arc = (θ/360) × 2πr.

How do you get the area of a circle with the diameter?

Answers. 1. The formula for the area A as a function of the diameter d of a circle is given by A = π (d/2)^2.