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Calculate the distance and midpoint between the given two points.
and
and
and
and
and
and
Determine the area of a circle whose diameter is defined by the given two points.
and
and
and
and
Rewrite in standard form and give the vertex.
Rewrite in standard form and graph. Be sure to find the vertex and all intercepts.
Determine the center and radius given the equation of a circle in standard form.
Determine standard form for the equation of the circle:
Center with radius
Center with radius
Center with radius
Center with radius
Circle whose diameter is defined by and
Circle whose diameter is defined by and
Find the x- and y-intercepts.
Graph.
Rewrite in standard form and graph.
Given the equation of an ellipse in standard form, determine its center, orientation, major radius, and minor radius.
Determine the standard form for the equation of the ellipse given the following information.
Center with and
Center with and
Center with and
Center with and
Find the x- and y-intercepts.
Graph.
Rewrite in standard form and graph.
Given the equation of a hyperbola in standard form, determine its center, which way the graph opens, and the vertices.
Determine the standard form for the equation of the hyperbola.
Center , , , opens up and down.
Center , , , opens left and right.
Center , , , opens left and right.
Center , , , opens up and down.
Find the x- and y-intercepts.
Graph.
Rewrite in standard form and graph.
Identify the conic sections and rewrite in standard form.
Given the graph, write the equation in general form.
Solve.
Distance: 5 units; midpoint:
Distance: units; midpoint:
Distance: units; midpoint:
square units
square units
; vertex:
; vertex:
; vertex:
; vertex:
;
;
;
;
;
Center: ; radius:
Center: ; radius:
x-intercepts: none; y-intercepts:
x-intercepts: ; y-intercepts:
x-intercepts: none; y-intercepts: ,
;
;
;
Center: ; orientation: horizontal; major radius: 4 units; minor radius: 2 units
Center: ; orientation: vertical; major radius: units; minor radius: 1 unit
x-intercepts: , ; y-intercepts:
x-intercepts: ; y-intercepts:
;
;
;
Center: ; opens left and right; vertices: ,
Center: ; opens upward and downward; vertices: ,
x-intercepts: ; y-intercepts: none
x-intercepts: ; y-intercepts: ,
;
;
;
Circle;
Hyperbola;
Ellipse;
Hyperbola;
Hyperbola;
,
,
,
, , ,
, , ,
Given two points and :
Determine the area of a circle whose diameter is defined by the points and
Rewrite in standard form and graph. Find the vertex and all intercepts if any.
Find the equation of a circle in standard form with center and radius units.
Sketch the graph of the conic section given its equation in standard form.
Rewrite in standard form and graph.
Find the x- and y-intercepts.
Solve.
Find the equation of an ellipse in standard form with vertices and and a minor radius 2 units in length.
Find the equation of a hyperbola in standard form opening left and right with vertices and a conjugate axis that measures 10 units.
Given the graph of the ellipse, determine its equation in general form.
A rectangular deck has an area of 80 square feet and a perimeter that measures 36 feet. Find the dimensions of the deck.
The diagonal of a rectangle measures centimeters and the perimeter measures 20 centimeters. Find the dimensions of the rectangle.
;
;
;
;
x-intercept: ; y-intercepts:
,
Ø
6 centimeters by 4 centimeters