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

Algebra ->  Sequences-and-series -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

5. a. Find the center and the radius of each circle
%28x+-+3%29%5E2+%2B+%28y+%2B+5%29%5E2+=+49
compare to formula for circle
%28x+-+h%29%5E2+%2B+%28y+-k%29%5E2+=+r%5E2 where h,k are coordinates of center, r+is radius

so, h=3, k=-5, and center is at (3,-5)
radius r=sqrt%2849%29=7


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

%28x-4%29%5E2%2F25+%2B+%28y%2B+6%29%5E2%2F49+=+1
compare to formula for vertical ellipse
%28x+-+h%29%5E2%2Fb%5E2+%2B+%28y+-k%29%5E2%2Fa%5E2+=1
h=4
k=-6
center at (4,-6)
the major axes length 2a=2%2Asqrt%2849%29=2%2A7+=14
and minor axes length 2b=2%2Asqrt%2825%29=2%2A+5=10



Answer by ikleyn(52788) About Me  (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
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(5)  The center of this circle is the point (3,-5).

     The radius of this circle is  sqrt%2849%29 = 7 units.



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

     The length of the major axis is 2%2Asqrt%2849%29 = 2*7 = 14 units.

     The length of the minor axis is 2%2Asqrt%2825%29 = 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.