What are vertices of the given ellipse?

V 1 ( 1 , 1 ) , V 2 ( − 7 , 1 ) V_1\left(1,1\right),\ V_2\left(-7,1\right) V 1 ( 1 , 1 ) , V 2 ( − 7 , 1 )

V 1 ( − 7 , 1 ) , V 2 ( 1 , 1 ) V_1\left(-7,1\right),\ V_2\left(1,1\right) V 1 ( − 7 , 1 ) , V 2 ( 1 , 1 )

V 1 ( − 1 , 1 ) , V 2 ( − 7 , 1 ) V_1\left(-1,1\right),\ V_2\left(-7,1\right) V 1 ( − 1 , 1 ) , V 2 ( − 7 , 1 )

V 1 ( 1 , 1 ) , V 2 ( 7 , 1 ) V_1\left(1,1\right),\ V_2\left(7,1\right) V 1 ( 1 , 1 ) , V 2 ( 7 , 1 )

Which among the following is the center of the ellipse described in the equation?

C ( 0 , 3 ) C\left(0,3\right) C ( 0 , 3 )

C ( 3 , 0 ) C\left(3,0\right) C ( 3 , 0 )

C ( − 3 , 0 ) C\left(-3,0\right) C ( − 3 , 0 )

C ( 0 , − 3 ) C\left(0,-3\right) C ( 0 , − 3 )

Find the correct asymptote for the given hyperbola.

y = ± 5 3 x y=\pm\frac{5}{3}x y = ± 3 5 x

y = ± 3 5 x y=\pm\frac{3}{5}x y = ± 5 3 x

y = ± 3 5 ( x − 3 ) y=\pm\frac{3}{5}\left(x-3\right) y = ± 5 3 ( x − 3 )

y = ± 5 3 ( x − 3 ) y=\pm\frac{5}{3}\left(x-3\right) y = ± 3 5 ( x − 3 )

Identify the proper vertices described in the given hyperbola.

V 1 ( 3 , 0 ) , V 2 ( − 3 , 0 ) V_1\left(3,0\right),\ V_2\left(-3,0\right) V 1 ( 3 , 0 ) , V 2 ( − 3 , 0 )

V 1 ( − 3 , 0 ) , V 2 ( 3 , 0 ) V_1\left(-3,0\right),\ V_2\left(3,0\right) V 1 ( − 3 , 0 ) , V 2 ( 3 , 0 )

V 1 ( 0 , 3 ) , V 2 ( 0 , − 3 ) V_1\left(0,3\right),\ V_2\left(0,-3\right) V 1 ( 0 , 3 ) , V 2 ( 0 , − 3 )

V 1 ( 0 , − 3 ) , V 2 ( 0 , 3 ) V_1\left(0,-3\right),\ V_2\left(0,3\right) V 1 ( 0 , − 3 ) , V 2 ( 0 , 3 )

Find the correct center and radius described by the equation.

r = 18 , C ( − 4 , 6 ) r\ =\ \sqrt{18},\ C\ \left(-4,6\right) r = 1 8 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , C ( − 4 , 6 )

r = 18 , C ( 4 , − 6 ) r\ =\ \sqrt{18},\ C\ \left(4,\ -6\right) r = 1 8 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , C ( 4 , − 6 )

r = 18 , C ( − 4 , 6 ) r=18,\ C\left(-4,6\right) r = 1 8 , C ( − 4 , 6 )

r = 18 , C ( 4 , − 6 ) r=18,\ C\ \left(4,\ -6\right) r = 1 8 , C ( 4 , − 6 )

CONIC SECTIONS

Authored by Hazelle Paulene

Mathematics

11th Grade

CCSS covered

Used 73+ times

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MULTIPLE CHOICE QUESTION

45 sec • 1 pt

The set of all points in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus) in the plane is called _______.

Circle

Parabola

Ellipse

Hyperbola

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Identify the type of conic section by inspection.

Circle

Parabola

Ellipse

Hyperbola

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

A conic section that has the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant.

Circle

Parabola

Ellipse

Hyperbola

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Identify the type of conic section.

Circle

Parabola

Ellipse

Hyperbola

Classify the conic section and its orientation is possible.

Ellipse, Vertical major axis

Hyperbola, Vertical tranverse axis

Parabola, opens to the Right

Parabola, opens to the Left

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

A type of conic section which has the set of all points that are equidistant from a fixed point in the plane.

Circle

Parabola

Ellipse

Hyperbola

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Find the focus of the given parabola.

$F\ \left(-1,5\right)$

$F\left(-1,1\right)$

$F\ \left(-1,3\right)$

$F\ \left(-1,-1\right)$

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CONIC SECTIONS

The set of all points in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus) in the plane is called _______.

Identify the type of conic section by inspection.

A conic section that has the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant.

Identify the type of conic section.

Classify the conic section and its orientation is possible.

A type of conic section which has the set of all points that are equidistant from a fixed point in the plane.

Find the focus of the given parabola.

By inspection, identify the type of conic section in this general form.

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