SOLUTION: 5. a. Find the center and the radius of each circle (𝑥 − 3)^2 + (𝑦 + 5)^2 = 49 b. For each ellipse, determine the coordinates of the centre, lengths of the major and

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Question 1206909: 5. a. Find the center and the radius of each circle
(𝑥 − 3)^2 + (𝑦 + 5)^2 = 49

b. For each ellipse, determine the coordinates of the centre, lengths of the major and minor axes.
(𝑥 − 4)^2/25 + (𝑦 + 6)^2/49 = 1

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

5. a. Find the center and the radius of each circle

compare to formula for circle
where , are coordinates of center, is radius

so, , , and center is at (,)
radius


b. For each ellipse, determine the coordinates of the center, lengths of the major and minor axes.


compare to formula for vertical ellipse



center at (,)
the major axes length
and minor axes length



Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
5. a. Find the center and the radius of each circle
(𝑥 − 3)^2 + (𝑦 + 5)^2 = 49
b. For each ellipse, determine the coordinates of the centre, lengths of the major and minor axes.
(𝑥 − 4)^2/25 + (𝑦 + 6)^2/49 = 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

(5)  The center of this circle is the point (3,-5).

     The radius of this circle is   = 7 units.



(6)  The center of this ellipse is the point (4,-6).

     The length of the major axis is  = 2*7 = 14 units.

     The length of the minor axis is  = 2*5 = 10 units.

Solved.

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On this subject, see the lessons
    - Ellipse definition, canonical equation, characteristic points and elements
    - Standard equation of an ellipse
    - Identify elements of an ellipse given by its standard equation
in this site.



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