Circles: 동영상 및 연습문제

Determine the graph that the equation represents.

$x^2+y^2=147$

Determine the graph that the equation represents.

$\(\frac{\left(x+24\right)^2}{72}\)+\(\frac{\left(y-37\right)^2}{72}\)=1$

Determine the graph that the equation represents.

$4x^2+64x+4y^2-48y=500$

Which statement best defines a circle in a Euclidean plane?

Given a circle centered at (4, -3) with a radius of 5, what is the equation of the circle?

What is the standard form equation of a circle centered at the origin with a radius of 7?

If the equation of a circle is (x - 2)^2 + (y + 5)^2 = 16, what is the center and radius of the circle?

Why does a circle fail the vertical line test?

Complete the square to rewrite the expression x^2 + 6x + 5 as a perfect square trinomial.

Which of the following points is the center of the circle with equation (x - 1)^2 + (y + 2)^2 = 25?

Given the equation (x + 5)^2 + (y - 6)^2 = 36, identify the center and radius of the circle.

What is the primary advantage of using the standard form of a circle's equation over the general form?

A circle is graphed with its center at (0, 0) and a point on the circle at (0, 7). What is the radius?

If a circle has a center at (-3, 4) and a radius of 10, what is its standard form equation?

Which geometric shape can be defined as a set of points equidistant from a central point?

Convert the equation x^2 + y^2 - 4x + 10y - 20 = 0 to standard form.

For the circle with equation (x - 7)^2 + (y + 3)^2 = 64, what are the coordinates of the center and the length of the radius?

What is a disadvantage of using the general form of a circle's equation compared to the standard form?

What is the radius of the circle with equation (x - 8)^2 + (y + 2)^2 = 100?

In the equation (x - 4)^2 + (y + 1)^2 = 49, what is the center of the circle?

The center of a circle is $(3,-2)$, and the point $(7,1)$ lies on the circle. Find $r^2$.

Write the standard-form equation of the circle with center $(-4,3)$ and radius $7$.

Convert $x^2+y^2-10x+6y-7=0$ to standard form.

In the process of converting $x^2+y^2+8x-14y+37=0$ to standard form, compute the value that ends up on the right side after completing the square for both variables (this is $r^2$ if a real circle exists).

Consider $(x+2{)}^2+(y-5{)}^2=-9$. How many real points are on this circle?

The circle $(x-2{)}^2+(y+1{)}^2=16$ has a topmost point. Find the $y$-coordinate of that point.

For the circle $x^2+y^2=25$, a vertical line $x=3$ intersects the circle in two points. Find the distance between those two intersection points.