Find the center and radius of the circle given by ${(x-7)}^2+{(y+2)}^2=121$.

Convert $x^2+y^2+6x-8y+9=0$ into standard form $(x-h{)}^2+(y-k{)}^2=R^2$.

Which first action is most appropriate when sketching a circle given in standard form ${(x-h)}^2+{(y-k)}^2=r^2$?

Which statement best describes how a circle can be considered a special case of an ellipse?

For the ellipse $\frac{x^2}{36}+\frac{y^2}{25}=1$, find the $y$-coordinates of the points on the ellipse with $x=3$.

For the ellipse $49x^2+36y^2=1764$, what are $a$, $b$, the direction of the major axis (horizontal or vertical), and the foci coordinates?

Which part of the vertex form equation $y=a(x-h{)}^2+k$ determines the horizontal position of the axis of symmetry for a vertical parabola?

Given the equation $y=(x+4{)}^2-3$, determine the vertex and the axis of symmetry of the parabola.

Find the vertex form of the vertical parabola with vertex $(3,-2)$ that passes through the point $(5,6)$.

In the standard equation $\frac{(x-h{)}^2}{a^2}-\frac{(y-k{)}^2}{b^2}=1$, what point is the center of the hyperbola?

A hyperbola is centered at the origin, opens left and right, has vertices at $(\pm 4,0)$, and its fundamental rectangle reaches $y=\pm 3$. What is its equation?

A researcher selects two points on the same hyperbola and measures their distances to the two foci. For the first point, the distances are $13$ and $5$. For the second point, the distances are $20$ and $12$. What is the best conclusion?