Circles and Ellipses

Write the equation of the circle with a Center at (5,3) that is tangent to the x-axis.

• $\left(x-3\right)^2+\left(y-5\right)^2=25$

• $\left(x-5\right)^2+\left(y-3\right)^2=25$

• $x^2+y^2=9$

• $\left(x-5\right)^2+\left(y-3\right)^2=9$

Find the equation of a circle with endpoints of a diameter (−3,1) and (9,-3).

•  $\left(x-3\right)^2+\left(y+1\right)^2=\sqrt{40}$ 

•  $\left(x+3\right)^2+\left(y-1\right)^2=40$ 

•  $\left(x-3\right)^2+\left(y+1\right)^2=40$ 

•  $x^2+y^2=\sqrt{29}$ 

Write the equation of the circle with a Center at (-2,5) that is tangent to the y-axis.

• $\left(x+2\right)^2+\left(y-5\right)^2=4$

• $\left(x+5\right)^2+\left(y-5\right)^2=25$

• $x^2+y^2=4$

• $\left(x-2\right)^2+\left(y+5\right)^2=25$

In the equation (x-4)²+(x-3)²=25, the center of the circle is at...

• (-3, -4)
• (4, 3)
• (-4, -3)
• (3, 4)

Tags

CCSS.HSG.GPE.A.1

The endpoints of a diameter of a circle are (3,1) and (9,5).Find the equation of the circle?

• $\left(x-6\right)^2+\left(y-3\right)^2=13$

• $\left(x-3\right)^2+\left(y-6\right)^2=132$

• $\left(x-6\right)^2+\left(y-3\right)^2=\sqrt{13}$

• $\left(x-9\right)^2+\left(y-5\right)^2=132$

Graph the ellipse:  $\frac{\left(x-4\right)^2}{16}+\frac{y^2}{49}=1$  

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In the equation (x+2)²+(y+3)²=49, the radius of the circle is...

• 14
• 98
• 7
• 49

Tags

CCSS.HSG.GPE.A.1

What are the major vertices of the ellipse in this picture?

• (2, 0), (–2, 0)
• (0, 2), (0, –2)
• (0, 4), (0, –4)
• (4, 0), (–4, 0)

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

What is the equation of the circle, with center (-4,5) and radius 6 units?

• (x - 4)² + (y + 5)² = 6
• (x - 4)² + (y + 5)² = 36
• (x + 4)² + (y - 5)² = 6
• (x + 4)² + (y - 5)² = 36