Exam 9: Analytic Geometry

Graph the equation. - $y^{2}=-20 x$ A) B) C) D)

Graph the equation. - $x^{2}=-18 y$ A) B) C) D)

Identify the equation without applying a rotation of axes. - $4 x ^ { 2 } + 5 x y + 2 y ^ { 2 } + 2 x + 3 y - 5 = 0$

Solve the problem. -An arch for a bridge over a highway is in the form of a semiellipse. The top of the arch is 35 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis) if the height 30 feet from the Center is to be 10 feet above ground?

Identify the equation without completing the square. - $2 x ^ { 2 } + 4 y ^ { 2 } - 3 x - 1 = 0$

Determine the appropriate rotation formulas to use so that the new equation contains no xy-term. - $11 x ^ { 2 } - 4 x y + 7 y ^ { 2 } - 8 x + 8 y = 0$ A) $x = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } - y ^ { \prime } \right)$ and $y = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } + y ^ { \prime } \right)$ B) $x = \frac { 1 } { 2 } x ^ { \prime } - \frac { \sqrt { 3 } } { 2 } y ^ { \prime }$ and $y = \frac { \sqrt { 3 } } { 2 } x ^ { \prime } + \frac { 1 } { 2 } y ^ { \prime }$ C) $x = - y ^ { \prime }$ and $y = x ^ { \prime }$ D) $x = \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } x ^ { \prime } - \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } y ^ { \prime }$ and $y = \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } x ^ { \prime } + \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } y ^ { \prime }$

Find an equation for the ellipse described. -Focus at $( 0 , - 4 )$ ; vertices at $( 0 , \pm 8 )$

Find an equation for the ellipse described. -Center $( 0,0 )$ ; major axis horizontal with length 10 ; length of minor axis is 4

Find an equation for the ellipse described. -Focus at $( - 3,0 )$ ; vertices at $( \pm 5,0 )$

Convert the polar equation to a rectangular equation. - $r = \frac { 4 \sec \theta } { 4 \sec \theta + 1 }$

Find an equation for the parabola described. -Vertex at (7, 8); focus at (3, 8) A) $( y - 8 ) ^ { 2 } = - 16 ( x - 7 )$ B) $( y - 8 ) ^ { 2 } = 16 ( x - 7 )$ C) $( x - 8 ) ^ { 2 } = 20 ( y - 8 )$ D) $( x - 8 ) ^ { 2 } = - 20 ( y - 8 )$

Graph the ellipse and locate the foci. - $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$

Graph the hyperbola. -A comet follows the hyperbolic path described by $\frac { x ^ { 2 } } { 22 } - \frac { y ^ { 2 } } { 22 } = 1$ , where $x$ and $y$ are in millions. If the sun is the fc of the path, how close to the sun is the vertex of the path?

Match the equation to the graph. - $( x + 2 ) ^ { 2 } = - 6 ( y + 2 )$

Graph the equation. - $4(x-1)^{2}+9(y+2)^{2}=36$

Solve the problem. -A race track is in the shape of an ellipse 80 feet long and 60 feet wide. What is the width 32 feet from the center?

Solve the problem. - $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 4 } = 1$

Determine the appropriate rotation formulas to use so that the new equation contains no xy-term. - $x ^ { 2 } + 2 x y + y ^ { 2 } - 8 x + 8 y = 0$

Find a rectangular equation for the plane curve defined by the parametric equations. - $y = 4 x - 5$

Rotate the axes so that the new equation contains no xy-term. Discuss the new equati - $x^{2}+x y+y^{2}-3 y-6=0$