Find any points of intersection of the graphs algebraically. $\begin{array} { l } - x ^ { 2 } + y ^ { 2 } + 2 x - 7 y + 6 = 0 \\ x ^ { 2 } + y ^ { 2 } - 2 x - 7 y + 6 = 0 \end{array}$

A) The points of intersection are \[( 2,2 )\] and $( 3,3 )$ . B) The points of intersection are $( - 2 , - 2 )$ and \[( 2,3 )\] . C) The points of intersection are $( 3,3 )$ and $( 3,3 )$ . D) The points of intersection are $( 2,2 )$ and $( 2,3 )$ . E) The points of intersection are $( 3,3 )$ and $( - 3 , - 3 )$ . A) The points of intersection are \[( 2,2 )\] and $( 3,3 )$ . B) The points of intersection are $( - 2 , - 2 )$ and \[( 2,3 )\] . C) The points of intersection are $( 3,3 )$ and $( 3,3 )$ . D) The points of intersection are $( 2,2 )$ and $( 2,3 )$ . E) The points of intersection are $( 3,3 )$ and $( - 3 , - 3 )$ .

Exam 63: Rotation of Conics

The $x ^ { \prime } y ^ { \prime }$ -coordinate system has been rotated $\theta$ degrees from the $x y$ -coordinate system.The coordinates of a point in the $x y$ -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. $\theta = 30 ^ { \circ }$ , $( 1,3 )$

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

C

Use the discriminant to classify the graph. $x ^ { 2 } - 10 x y - 8 y ^ { 2 } - 18 = 0$

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

B

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $24 x ^ { 2 } + 66 x y + 13 y ^ { 2 } = 32$

Free

(Multiple Choice)

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Question 3

Correct Answer:

Verified

D

Find the lengths of the major and minor axes of the ellipse graphed by following equation. $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 1 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1$

(Multiple Choice)

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Question 4

Select the graph of the following equation. $y = x \pm 5$

(Multiple Choice)

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Question 5

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $3 x ^ { 2 } - 9 x y + 11 y ^ { 2 } + ( 3 \sqrt { 10 } - 9 ) x - ( 5 \sqrt { 10 } + 10 ) y = 91$

(Multiple Choice)

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Question 6

Use the Quadratic Formula to solve for $y$ . $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 0$

(Multiple Choice)

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Question 7

The $x ^ { \prime } y ^ { \prime }$ -coordinate system has been rotated $\theta$ degrees from the $x y$ -coordinate system.The coordinates of a point in the $x y$ -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. $\theta = 45 ^ { \circ }$ , $( 9,2 )$

(Multiple Choice)

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Question 8

Select the graph of degenerate conic. $x ^ { 2 } + y ^ { 2 } - 2 x + 16 y + 65 = 0$

(Multiple Choice)

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Question 9

Select the graph of the following equation,showing both sets of axes. $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 8 } - \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 8 } = 1$

(Multiple Choice)

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Question 10

Use the Quadratic Formula to solve for $y$ . $81 x ^ { 2 } - 90 x y + 25 y ^ { 2 } + 10 y = 0$

(Multiple Choice)

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Question 11

Use the Quadratic Formula to solve for $y$ . $x ^ { 2 } - 12 x y - 10 y ^ { 2 } - 22 = 0$

(Multiple Choice)

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Question 12

Use a graphing utility to graph the conic. $x ^ { 2 } - 4 x y + 2 y ^ { 2 } = 8$

(Multiple Choice)

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Question 13

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $29 x ^ { 2 } + 92 x y + 6 y ^ { 2 } = 51$

(Multiple Choice)

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Question 14

Use the discriminant to classify the graph. $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 0$

(Multiple Choice)

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Question 15

The $x ^ { \prime } y ^ { \prime }$ -coordinate system has been rotated $\theta$ degrees from the $x y$ -coordinate system.The coordinates of a point in the $x y$ -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. $\theta = 90 ^ { \circ }$ , $( 0,3 )$

(Multiple Choice)

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Question 16

Identify the conic by writing the equation in standard form. $10 y ^ { 2 } - 20 x ^ { 2 } + 80 y + 360 x - 1485 = 0$

(Multiple Choice)

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Question 17

Find any points of intersection of the graphs algebraically. -++2x-7y+6=0 +-2x-7y+6=0

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Question 18

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. $x y + 3 = 0$

(Multiple Choice)

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Question 19

Use the discriminant to classify the graph. $16 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 0$

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Question 20

Exam 63: Rotation of Conics

Use the discriminant to classify the graph.​ x2−10xy−8y2−18=0x ^ { 2 } - 10 x y - 8 y ^ { 2 } - 18 = 0x2−10xy−8y2−18=0 ​

Determine the angle θ\thetaθ through which the axes are rotated.Round your answer to two decimal places.​ 24x2+66xy+13y2=3224 x ^ { 2 } + 66 x y + 13 y ^ { 2 } = 3224x2+66xy+13y2=32 ​

Find the lengths of the major and minor axes of the ellipse graphed by following equation.​ (x′)21+(y′)236=1\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 1 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 11(x′)2​+36(y′)2​=1 ​

Select the graph of the following equation.​ y=x±5y = x \pm 5y=x±5 ​

​Determine the angle θ\thetaθ through which the axes are rotated.Round your answer to two decimal places. 3x2−9xy+11y2+(310−9)x−(510+10)y=913 x ^ { 2 } - 9 x y + 11 y ^ { 2 } + ( 3 \sqrt { 10 } - 9 ) x - ( 5 \sqrt { 10 } + 10 ) y = 913x2−9xy+11y2+(310​−9)x−(510​+10)y=91 ​​

Use the Quadratic Formula to solve for yyy .​ 5x2+10xy+11y2+9x−10y−42=05 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 05x2+10xy+11y2+9x−10y−42=0 ​

Select the graph of degenerate conic.​ x2+y2−2x+16y+65=0x ^ { 2 } + y ^ { 2 } - 2 x + 16 y + 65 = 0x2+y2−2x+16y+65=0 ​

Select the graph of the following equation,showing both sets of axes.​ (x′)28−(y′)28=1\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 8 } - \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 8 } = 18(x′)2​−8(y′)2​=1 ​

Use the Quadratic Formula to solve for yyy .​ 81x2−90xy+25y2+10y=081 x ^ { 2 } - 90 x y + 25 y ^ { 2 } + 10 y = 081x2−90xy+25y2+10y=0 ​

Use the Quadratic Formula to solve for yyy .​ x2−12xy−10y2−22=0x ^ { 2 } - 12 x y - 10 y ^ { 2 } - 22 = 0x2−12xy−10y2−22=0 ​

Use a graphing utility to graph the conic.​ x2−4xy+2y2=8x ^ { 2 } - 4 x y + 2 y ^ { 2 } = 8x2−4xy+2y2=8 ​

Determine the angle θ\thetaθ through which the axes are rotated.Round your answer to two decimal places.​ 29x2+92xy+6y2=5129 x ^ { 2 } + 92 x y + 6 y ^ { 2 } = 5129x2+92xy+6y2=51 ​

Use the discriminant to classify the graph.​ 5x2+10xy+11y2+9x−10y−72=05 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 05x2+10xy+11y2+9x−10y−72=0 ​

Identify the conic by writing the equation in standard form. 10y2−20x2+80y+360x−1485=010 y ^ { 2 } - 20 x ^ { 2 } + 80 y + 360 x - 1485 = 010y2−20x2+80y+360x−1485=0

Find any points of intersection of the graphs algebraically.​ -++2x-7y+6=0 +-2x-7y+6=0 ​

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form.​ xy+3=0x y + 3 = 0xy+3=0 ​

Use the discriminant to classify the graph.​ 16x2−5xy+10y2−44=016 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 016x2−5xy+10y2−44=0 ​

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Introduction to Conics Parabolas

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Use the discriminant to classify the graph. $x ^ { 2 } - 10 x y - 8 y ^ { 2 } - 18 = 0$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $24 x ^ { 2 } + 66 x y + 13 y ^ { 2 } = 32$

Find the lengths of the major and minor axes of the ellipse graphed by following equation. $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 1 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1$

Select the graph of the following equation. $y = x \pm 5$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $3 x ^ { 2 } - 9 x y + 11 y ^ { 2 } + ( 3 \sqrt { 10 } - 9 ) x - ( 5 \sqrt { 10 } + 10 ) y = 91$

Use the Quadratic Formula to solve for $y$ . $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 42 = 0$

Select the graph of degenerate conic. $x ^ { 2 } + y ^ { 2 } - 2 x + 16 y + 65 = 0$

Select the graph of the following equation,showing both sets of axes. $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 8 } - \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 8 } = 1$

Use the Quadratic Formula to solve for $y$ . $81 x ^ { 2 } - 90 x y + 25 y ^ { 2 } + 10 y = 0$

Use the Quadratic Formula to solve for $y$ . $x ^ { 2 } - 12 x y - 10 y ^ { 2 } - 22 = 0$

Use a graphing utility to graph the conic. $x ^ { 2 } - 4 x y + 2 y ^ { 2 } = 8$

Determine the angle $\theta$ through which the axes are rotated.Round your answer to two decimal places. $29 x ^ { 2 } + 92 x y + 6 y ^ { 2 } = 51$

Use the discriminant to classify the graph. $5 x ^ { 2 } + 10 x y + 11 y ^ { 2 } + 9 x - 10 y - 72 = 0$

Identify the conic by writing the equation in standard form. $10 y ^ { 2 } - 20 x ^ { 2 } + 80 y + 360 x - 1485 = 0$

Find any points of intersection of the graphs algebraically. -++2x-7y+6=0 +-2x-7y+6=0

Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. $x y + 3 = 0$

Use the discriminant to classify the graph. $16 x ^ { 2 } - 5 x y + 10 y ^ { 2 } - 44 = 0$