Equations of Circles Review

What is the standard form of the equation of a circle?

• (x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius.

• (x-h)² + (y-k)² = 2r, where (h,k) is the center and r is the radius.

• x² + y² = r², where (0,0) is the center and r is the radius.

• (x+h)² + (y+k)² = r², where (h,k) is the center and r is the radius.

What is the relationship between the coefficients of x and y in the general form of a circle's equation?

• A must be equal for the equation to represent a circle.

• A can be any value for the equation to represent a circle.

• B must be equal to C for the equation to represent a circle.

• The coefficients of x and y have no relationship in the equation.

What is the radius of the circle represented by the equation (x-5)² + (y+1)² = 36?

• 4

• 5

• 6

• 7

What is the equation of a circle with center (0,0) and radius 4?

• x² + y² = 16

• (x - 4)² + (y - 4)² = 16

• x² + y² = 8

• (x + 4)² + (y + 4)² = 16

What does the term 'completing the square' mean in the context of circles?

• A method to find the area of a circle.

• A technique to rewrite a quadratic equation in standard form, making it easier to identify the center and radius.

• A way to calculate the circumference of a circle.

• A process to determine the diameter of a circle.

How can you determine if a point lies inside, on, or outside a circle?

• Substitute the point's coordinates into the circle's equation. If the result is less than r², it's inside; equal to r², it's on; greater than r², it's outside.

• Measure the distance from the point to the center of the circle and compare it to the radius.

• Check if the point's coordinates are positive or negative.

• Use the slope of the line connecting the point to the center of the circle.

How do you convert the general form of a circle's equation to standard form?

• By factoring the equation into linear terms.

• By completing the square for x and y.

• By using the quadratic formula to find the roots.

• By rearranging the equation to isolate y.

How do you find the center of a circle from its equation?

• Identify the values of h and k from the equation (x-h)² + (y-k)² = r².

• Calculate the diameter of the circle and divide by two.

• Use the coordinates of any point on the circle to find the center.

• Determine the slope of the line tangent to the circle.

What does the equation (x-4)² + (y+4)² = 25 represent?

• A line with slope 5

• A circle with center (4, -4) and radius 5

• A parabola opening upwards

• An ellipse with foci at (4, -4) and (0, 0)

What is the center of the circle in the equation (x-3)² + (y-2)² = 16?

• (3, 2)

• (2, 3)

• (4, 4)

• (1, 1)