d. L'equazione \( x^{2}+y^{2}+12 x=0 \) ha il centro sull'asse \( y \). Scrivi l'equazione della circonferenza di centro \( C(1 ;-2) \) che ha lo stesso raggio della circonferenza di equa- zione \( x^{2}+y^{2}-6 y+5=0 \) e rappresenta graficamente le due circonferenze. \( \left[x^{2}+y^{2}-2 x+4 y+1=0\right] \)

Graph the hyperbola \( x^{2}-y^{2}=36 \). Give the domain, range, center, vertices, foci, and e asymptotes for the figure. The hyperbola has a center at (Type an ordered pair.) The vertices are 21. (Type ordered pairs. Use a comma to separate answers as needed.) The foci are \( (6 \sqrt{2.0}),(-6 \sqrt{2,0}) \). (Type ordered pairs. Type an exact answer, using radicals as needed. Use a comma to \( s \) answers as needed.) What are the equations of the asymptotes? Choose the correct answer below. A. \( y= \pm 6 x \) B. \( x= \pm 6 y \) C. \( x= \pm y \) (O). \( y= \pm x \)

Identify the type of graph for the equation. \( 5(x-1)^{2}+5(y+1)^{2}=0 \) What type of graph is described by this equation? A. Circle B. Point C. Ellipse D. No graph

\begin{tabular}{l|l} Identify the type of graph that the equation has, without graphing. \\ \( \frac{x^{2}}{81}-\frac{y^{2}}{81}=1 \) & \( \begin{array}{r}\text { This equation ha } \\ \text { A parabola } \\ \text { A hyperbo } \\ \text { An ellipse }\end{array} \) \\ Acircle \end{tabular}

Nrite an equation for the given ellipse that satisfies the following cond Center at \( (5,4) \); minor axis vertical, with length \( 8 ; c=3 \). The equation for the given ellipse is (Type your answer in standard form.)

A one-way road passes under an overpass in the shape of half an ellipse, 20 ft high at the center and 20 ft wide. Ass 17 of 21 what is the tallest truck that can pass under the overpass? The tallest truck that can pass under the overpass is \( \square \mathrm{ft} \) tall.