Classify the conic section.

• Circle

• Ellipse

• Line

• None of these

Answer explanation

A circle is a special case of an ellipse where the two foci coincide, resulting in all points being equidistant from the center. Therefore, the correct classification of the conic section is a Circle.

Tags

CCSS.HSG.GPE.A.1

Is the hyperbola vertical or horizontal? 

• Vertical

• Horizontal

Answer explanation

The hyperbola is vertical because its equation is in the form (y-k)²/a² - (x-h)²/b² = 1, indicating that it opens upwards and downwards. This confirms the correct choice is 'Vertical'.

Tags

CCSS.HSG.GPE.A.3

What is the radius of (x + 2)² +(y - 5)² = 5

• 5

• 25

• √5

• (-2,5)

Answer explanation

The equation (x + 2)² + (y - 5)² = 5 represents a circle centered at (-2, 5) with radius √5. The radius is determined by the value on the right side of the equation, which is 5, and the radius is √5.

Tags

CCSS.HSG.GPE.A.1

Identify the center and the length of a and b.

• C: (0,0)  a= 25, b=4

• C: (0,0)  a= 4, b=25

• C: (0,0)  a= 2, b=5

• C: (0,0)  a= 5, b=2

Answer explanation

The center of the ellipse is at (0,0). The lengths of the semi-major and semi-minor axes are given as a=5 and b=2, which corresponds to the correct choice. The other options do not match these values.

Tags

CCSS.HSG.GPE.A.1

Center ?

• (-3 , 2)

• (2 , -3)

• (12 , 5)

• (5 , 12)

Answer explanation

The center of a circle is given as a point (h, k). The correct choice, (-3, 2), represents the center of a circle, while the other options do not match this format. Thus, (-3, 2) is the correct answer.

Tags

CCSS.HSG.GPE.A.1

Find the standard equation of the given ellipse

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Tags

CCSS.HSG.GPE.A.1

Find the standard equation of the given ellipse

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Tags

CCSS.HSG.GPE.A.1

Which conic's equation has only 1 squared term?

• Parabola

• Circle

• Ellipse

• Hyperbola

Answer explanation

A parabola is defined by an equation with only one squared term, such as y = ax^2. In contrast, circles, ellipses, and hyperbolas have two squared terms, making the parabola the only conic with just one.

Tags

CCSS.HSG.GPE.A.2

Determine the equation of the hyperbola.

Answer explanation

The correct equation of the hyperbola is \(\frac{x^2}{4}-\frac{y^2}{1}=1\) because it follows the standard form \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) with \(a^2=4\) and \(b^2=1\).

Tags

CCSS.HSG.GPE.A.3

What is the equation used to find the focal points on an ELLIPSE?

• c² = a² + b²

• c² = a² - b²

• 1/4d

• (x-h)² + (y-k)² = r²

Answer explanation

The correct equation for finding the focal points of an ellipse is c² = a² - b², where c is the distance from the center to a focus, a is the semi-major axis, and b is the semi-minor axis.

Tags

CCSS.HSG.GPE.A.1