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Hotmath
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Hotmath
Chapter: Quadratic Relations/Analytic Geometry Section: Classifying Conics
 

Problem: 1

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

x 2 + 6 x y + 5 = 0.

 

Problem: 3

Tell which conic is defined by the equation

4 x 2 + y 2 – 8 x – 2 y = –1.

 

Problem: 5

Tell which conic is defined by the equation

y 2 – 2 x 2 + 2 x + 2 y = 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

Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 and find the values of A , B , C , D , E , and F .

 

Problem: 9

Classify the conic section.

8 x 2 + 5 y 2 + 16 x – 28 y + 16 = 0

 

Problem: 11

Classify the conic section.

9 x 2 – 16 y 2 + 20 y + 4 x = 0

 

Problem: 13

Classify the conic section.

2 x 2 – 3 x + 9 y + 10 = 0

 

Problem: 15

Classify the conic section.

2 x 2 + 2 y 2 – 5 x – 3 y – 5 = 0

 

Problem: 17

Identify the type of conic.

9 x 2 + 25 y 2 – 36 x – 50 y + 61 = 0


Problem: 19

Identify the type of conic.

x 2 – 9 y 2 + 13 x – 67 y – 94 = 0

 

Problem: 21

Identify the type of conic.

3 x 2 – 5 x + 7 y + 11 = 0


Problem: 23

Identify the type of conic.

4 x 2 + 4 y 2 – 7 x – 5 y – 4 = 0


Problem: 25

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

y 2 – 18 y + 9 x + 9 = 0

 

Problem: 27

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

4 x 2 y 2 – 24 x + 6 y + 23 = 0

 

Problem: 29

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

x 2 + 9 y 2 – 4 x – 36 y + 31 = 0

 

Problem: 31

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

x 2 + y 2 – 10 x – 10 y + 25 = 0

 

Problem: 33

Sketch the graph of the equation.

13 x 2 + 13 y 2 – 182 x – 52 y + 572 = 0

 

Problem: 35

Sketch the graph of the equation.

–16 x 2 + 9 y 2 + 64 x + 144 y + 496 = 0

 

Problem: 37

Find the point of intersection.

4 x 2 + y 2 – 48 x – 2 y + 129 = 0

x 2 + y 2 – 2 x – 2 y – 7 = 0

 

Problem: 39

Find the point of intersection.

4 x 2 + y 2 + 40 x – 28 y + 40 = 0

4 x 2 + y 2 + 72 x – 28 y + 456 = 0

 

Problem: 41

Find the point of intersection.

y 2 – 2 x – 10 y + 31 = 0

x y + 2 = 0