1. write the equation in standard form. identify the important features of the graph:
x^2+y^2-9x+10y+15=0

2. write the equation in standard form. identify the important features of the graph:
y^2+4y-8x+4=0

3. write the equation of the conic section with the given properties:
a hyperbola with vertices, (0, -6) and (0,6), asymptotes, y=3/4 x and y = -3/4 x

4. write the equation of the conic section with the given properties:
an ellipse with vertices, (0,-5) and (0,5), and a minor axis of length 8.

Step-by-step explanation:

1. Complete the square for both x and y by adding a constant equal to the square of half the linear term coefficient. Subtract 15, and rearrange to standard form.

  (x^2 -9x +4.5^2) +(y^2 +10y +5^2) = 4.5^2 +5^2 -15

  (x -4.5)^2 +(y +5)^2 = 30.25 . . . . . write in standard form

Important features: center = (4.5, -5); radius = 5.5.

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2. To put this in the form x=f(y), we need to add 8x, then divide by 8.

  x = (1/8)y^2 +(1/2)y +(1/2)

Important features: vertex = (0, -2); focus = (2, -2); horizontal compression factor = 1/8.

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3. We want y^2/a^2 -x^2/b^2 = 1 with a=36 and b=(36/(3/4)^2) = 64:

  y^2/36 -x^2/64 = 1

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4. In the form below, "a" is the semi-axis in the x-direction. Here, that is 8/2 = 4. "b" is the semi-axis in the y-direction, which is 5 in this case. We want x^2/a^2 +y^2/b^2 = 1 with a=4 and b=5.

  x^2/16 +b^2/25 = 1

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The first attachment shows the circle and parabola; the second shows the hyperbola and ellipse.

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )

step-by-step explanation: