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wel
3 years ago
15

identify the graph of 9x^2-25y^2=225 for t(0 5) and write an equation of the translated or rotated graph in general form

Mathematics
2 answers:
tamaranim1 [39]3 years ago
5 0

ANSWER

The required equation is:

9 {x}^{2}  - 25{y}^{2}  + 250y  - 85 0=0

EXPLANATION

The given equation is

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

Dividing through by 225 we obtain;

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

This is a hyperbola that has it's centre at the origin.

If this hyperbola is translated so that its center is now at (0,5).

Then its equation becomes:

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

We multiply through by 225 to get;

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

We now expand to get;

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

9 {x}^{2}  - 25{y}^{2}  + 250y  - 6 25 = 225

The equation of the hyperbola in general form is

9 {x}^{2}  - 25{y}^{2}  + 250y  - 85 0=0

Pavel [41]3 years ago
5 0

Answer:

It's C) hyperbola; 9x^2-25y^2+250y-850=0

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