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

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

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

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

(h, k) = (- 1, 2), a = \frac{5}{2}, b = 5

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 2), a = \frac{5}{2}, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 2), b = 5, a = \frac{5}{2}

2 x^{2} + y^{2} - 7 = 0

x^{2} + 2 y^{2} - 8 x + 8 y = 20

3 x^{2} + 3 y^{2} - 12 y = 0

4 x^{2} + 49 y^{2} = 196

x^{2} + 8 (y + 5)^{2} = 20

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