What is 25(x-1)^2+(y-1)^2=25 ?

The solution to 25(x-1)^2+(y-1)^2=25 is Ellipse with (h,k)=(1,1),a=1,b=5

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25(x-1)^2+(y-1)^2=25

25 (x - 1)^{2} + (y - 1)^{2} = 25

(h, k) = (1, 1), a = 1, b = 5

Solution steps

25 (x - 1)^{2} + (y - 1)^{2} = 25

Rewrite

25 (x - 1)^{2} + (y - 1)^{2} = 25

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{1 ^{2}} + \frac{( y - 1 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 1), a = 1, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 1), b = 5, a = 1

25 x^{2} + 16 y^{2} + 100 x + 32 y - 284 = 0

4 X^{2} + 8 Y^{2} - 24 X + 32 Y - 12 = 0

\frac{( x + 2 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{20} = 1

\frac{( x + 2 ) ^{2}}{4 ^{2}} + \frac{( y - 1 ) ^{2}}{5 ^{2}} = 1

x^{2} + y^{2} = - y^{2} + 4

What is 25(x-1)^2+(y-1)^2=25 ?
The solution to 25(x-1)^2+(y-1)^2=25 is Ellipse with (h,k)=(1,1),a=1,b=5