Circles and Ellipses Applications

What is the center of the ellipse?

• (0, 0)
• (1, 5)
• (1, 0)
• (0, 1)

Write the standard form of the ellipse:

9x² + 4y² +72x +108=0

• (x-4)² /16 + y ²/ 36 = 1

• (x+4)² /4 + y ²/ 9 = 1

• (x-4)² /4 + y ²/ 9 = 1

• (x+4)² /16 + y ²/ 36 = 1

Identify the center and the length of a and b.

• C: (0,4)  a= 25, b=4
• C: (0,0)  a= 4, b=25
• C: (0,5)  a= 2, b=5
• C: (0,0)  a= 5, b=2

Write the equation of a circle with center (7, 0) with radius 3.

• (x - 7)² + y² = 9
• x² + (y -7)² = 9
• (x - 7)² + y² = 3
• x² + (y -7)² = 3

What is the equation of the circle?

• (x+1)² + (y +1)² = 3
• (x+1)² + (y -1)² = 3
• (x+1)² + (y +1)² = 9
• (x-1)² + (y -1)² = 9

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

• (x - 2)² + (y + 5)² = 36

• (x + 5)² + (y - 2)² = 144

• (x + 5)² + (y - 2)² = 36

• (x + 2)² + (y - 5)² = 6

The point (-3, 4) is on a circle with center (1, -1). Write the standard equation of the circle.

• (x + 1)² + (y - 1)² = 41

• (x - 1)² + (y + 1)² = 16

• (x + 1)² + (y - 1)² = 1681

• (x - 1)² + (y + 1)² = 41

The equation of a circle is given. Use completing the square to write the equation in standard form.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

• 4
• 2
• 3
• 16

Which is the equation of the circle graphed below?

• (x - 3)² + (y + 4)² = 9

• (x - 3)² + (y + 4)² = 3

• (x)² + (y)² = 9

• (x - 1)² + (y + 1)² = 7