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Ahat [919]
3 years ago
10

Write an equation of the ellipse with foci at (0, ±9), and vertices at (0, ±13).

Mathematics
1 answer:
alisha [4.7K]3 years ago
4 0

Write an equation of the ellipse with focus at (0,+-9) and vertices at (0,+-13)

The major axis is along  the  y-axis

We need to find " b"  = √[a^2  − c^2] =  √ [ 13^2 − 9^2]  = √ [169 − 81]  = √88

So.... the equation is

y^2 / a^2     +     x^2 / b^2      =   1

y^2 / 169   +     x^2 / 88      =   1

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Answer:

The correct option is the first option;

Triangle XYZ and PYT are connected at point Y. Triangle XYZ is reflected across XY and then is reflected another time across YZ to form triangle PYT

Step-by-step explanation:

To answer the question we look at each option as follows;

1) The parameters given are triangle XYZ and PYT are connected at point Y

Triangle XY is reflected about XY will shift the marked angle from left to right while the right angle will remain at the same location and the triangle will remain upright to give triangle X'Y'Z'

Reflection about the YZ will give; the marked angle and the right angle in the same location and the vertex X will then be changed to P

Therefore, triangle XYZ can be mapped to triangle PYT with two reflections

2)  In the second option, we have triangle XYZ is reflected 3 times which is more than 2 times as in the question, therefore, option two is less suited as an answer to the question

3) Triangle XYZ is reflected across side XY and then is shifted down to form triangle AYT

Therefore, since we have only one reflection, option 3 is also not appropriate as an answer

4) In option 4 triangle XYZ is reflected and then rotated therefore option 4 is also not a correct option.

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