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Hotmath Practice Problems

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Title:
Hotmath Algebra 2
Author:
Hotmath Team
 
Free
Chapter:Quadratic Relations/Analytic GeometrySection:Classifying Conics
 

Problem: 1

Tell which conic (circle, parabola, hyperbola, or ellipse) is defined by the equation

x2 + 6xy + 5 = 0.

 

Problem: 3

Tell which conic is defined by the equation

4x2 + y2– 8x – 2y = –1.

 

Problem: 5

Tell which conic is defined by the equation

y2 – 2x2 + 2x + 2y = 9.

 

Problem: 7

A circle with equation (x – 120)2 + (y – 150)2 = 19600 is given. Expand and simplify the binomials in this equation in order to get an equation of the form

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 and find the values of A, B,C, D, E, and F.

 

Problem: 9

Classify the conic section.

8x2 + 5y2 + 16x – 28y + 16 = 0

 

Problem: 11

Classify the conic section.

9x2 – 16y2 + 20y + 4x = 0

 

Problem: 13

Classify the conic section.

2x2 – 3x + 9y + 10 = 0

 

Problem: 15

Classify the conic section.

2x2 + 2y2 – 5x – 3y – 5 = 0

 

Problem: 17

Identify the type of conic.

9x2 + 25y2 – 36x – 50y + 61 = 0


Problem: 19

Identify the type of conic.

x2 – 9y2 + 13x – 67y – 94 = 0

 

Problem: 21

Identify the type of conic.

3x2 – 5x + 7y + 11 = 0


Problem: 23

Identify the type of conic.

4x2 + 4y2 – 7x – 5y – 4 = 0


Problem: 25

Classify the conic section and find its equation in the standard form. Also graph the equation.

y2 – 18y + 9x + 9 = 0

 

Problem: 27

Categorsie the conic section, write its equation in the standard form, and graph it.

4x2y2 – 24x + 6y + 23 = 0

 

Problem: 29

Categorize the conic section and write its equation in the standard form and graph the equation.

x2 + 9y2 – 4x – 36y + 31 = 0

 

Problem: 31

Categorize the conic section and write its equation in the standard form and graph the equation.

x2 + y2 – 10x – 10y + 25 = 0

 

Problem: 33

Sketch the graph of the equation.

13x2 + 13y2 – 182x – 52y + 572 = 0

 

Problem: 35

Sketch the graph of the equation.

–16x2 + 9y2 + 64x + 144y + 496 = 0

 

Problem: 37

Find the point of intersection.

4x2 + y2 – 48x – 2y + 129 = 0

x2 + y2 – 2x – 2y – 7 = 0

 

Problem: 39

Find the point of intersection.

4x2 + y2 + 40x – 28y + 40 = 0

4x2 + y2 + 72x – 28y + 456 = 0

 

Problem: 41

Find the point of intersection.

y2 – 2x – 10y + 31 = 0

xy + 2 = 0