What is (x-2)^2+(2y+3)^2=26 ?

The solution to (x-2)^2+(2y+3)^2=26 is Ellipse with (h,k)=(2,-3/2),a=sqrt(26),b=sqrt(13/2)

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(x-2)^2+(2y+3)^2=26

(x - 2)^{2} + (2 y + 3)^{2} = 26

(h, k) = (2, - \frac{3}{2}), a = 26, b = \frac{13}{2}

Solution steps

(x - 2)^{2} + (2 y + 3)^{2} = 26

Rewrite

(x - 2)^{2} + (2 y + 3)^{2} = 26

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 26 ) ^{2}} + \frac{( y - ( - \frac{3}{2} ) ) ^{2}}{( \frac{13}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - \frac{3}{2}), a = 26, b = \frac{13}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - \frac{3}{2}), a = 26, b = \frac{13}{2}

144 = 4 x^{2} + y^{2}

9 x^{2} + 18 x + 16 y^{2} - 64 y - 71 = 0

16 x^{2} + 36 y^{2} - 96 x + 144 y + 144 = 0

9 x^{2} + 36 x + 16 y^{2} - 96 y = - 36

4 - 12 x^{2} - 36 y^{2} \geq 0

What is (x-2)^2+(2y+3)^2=26 ?
The solution to (x-2)^2+(2y+3)^2=26 is Ellipse with (h,k)=(2,-3/2),a=sqrt(26),b=sqrt(13/2)