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Vera_Pavlovna [14]
3 years ago
13

Q1: Identify the graph of the equation and write an equation of the translated or rotated graph in general form.

Mathematics
1 answer:
marin [14]3 years ago
3 0

Answer:

C. hyperbola; 9x^2-25y^2-250y-850=0

Step-by-step explanation:

The given conic has equation:

9x^2-25y^2=225

Divide through by 225.

\frac{9x^2}{225}-\frac{25y^2}{225}=\frac{225}{225}

\frac{x^2}{25}-\frac{y^2}{9}=1

This is a hyperbola centered at the origin.

The hyperbola has been translated from the origin to (0,5).

The translated hyperbola will have equation;

\frac{(x-0)^2}{25}-\frac{(y-5)^2}{9}=1

Multiply through by 225.

9(x-0)^2-25(y-5)^2=225

Expand

9x^2-25(y^2-10y+25)=225

9x^2-25y^2+250y-625=225

Rewrite in general form;

9x^2-25y^2+250y-625-225=0

9x^2-25y^2+250y-850=0

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Tanya run 50 yards across the diagonal of the rectangular field.

<u>Step-by-step explanation</u>:

Step 1 :

  • Length of the rectangular field = 40 yards
  • width of the rectangular field = 30 yards

Step 2 :

Measure of the diagonal = √(length^2 + width^2 )

Step 3 :

Diagonal = √(40^2 + 30^2 )

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Step 4 :

Since distance cannot be negative, The measure of diagonal = 50 yards.

∴ Tanya runs diagonally across a rectangular field is 50 yards.

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