randRangeNonZero( -30, 30 ) / 10
randRange( -30, 30 ) / 10
randRange( -70, 70 ) / 10
function( x ) {
return A*x*x + B*x + C;
}
Identify this conic section. Give the most specific name.
graphInit({
range: 10,
scale: 20,
tickStep: 1,
axisArrows: "<->"
});
style({ stroke: "#6495ED" });
Parabola
- Parabola
- Hyperbola
- Circle
- Ellipse
This graph has a vertex and is U-shaped. It extends to infinity on both ends.
That describes a parabola.
randRangeNonZero(10, 70) / 10
randRangeNonZero(10, 70) / 10
randRangeNonZero(-30, 30) / 10
randRangeNonZero(-30, 30) / 10
function( t ) {
return [ A * cos( t ) + C, B * sin( t ) + D ];
}
plotParametric( PARA_FUNC, [-PI, PI] );
Ellipse
You can see that the graph resembles a squished circle.
This shape is an ellipse.
randRangeNonZero( -70, 70 ) / 10
A
Circle
This shape is perfectly round and symmetrical. All the points on it are equidistant from its center.
A circle has those properties.
randRangeNonZero( -40, 40 ) / 10
randRangeNonZero( -40, 40 ) / 10
function( t ) {
return [ A / cos( t ), B * tan( t ) ];
}
// to steer clear of discontinuities,
// split up the plotting and add some buffer area away from them
plotParametric( PARA_FUNC, [-PI, -PI/2-0.1] );
plotParametric( PARA_FUNC, [-PI/2+0.1, PI/2-0.1] );
plotParametric( PARA_FUNC, [PI/2+0.1, PI] );
Hyperbola
This graph has two asymptotes which it approaches. It's also U-shaped on each side.
plot( function( x ) { return (B/A) * x; }, [-10, 10], { stroke: "gray" } );
plot( function( x ) { return (B/A) * -1 * x; }, [-10, 10], { stroke: "gray" } );
This conic section is therefore a hyperbola.