What is ((x-1)/2)^2+(y+3)^2= 49/64 ?

The solution to ((x-1)/2)^2+(y+3)^2= 49/64 is Ellipse with (h,k)=(1,-3),a= 7/4 ,b= 7/8

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((x-1)/2)^2+(y+3)^2= 49/64

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

(h, k) = (1, - 3), a = \frac{7}{4}, b = \frac{7}{8}

Solution steps

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

Rewrite

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( \frac{7}{4} ) ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( \frac{7}{8} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 3), a = \frac{7}{4}, b = \frac{7}{8}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 3), a = \frac{7}{4}, b = \frac{7}{8}

x^{2} + y^{2} = 2 \cdot \frac{y}{x ^{2} + y ^{2}}

16 x^{2} + 25 y^{2} - 64 x - 150 y - 11 = 0

36 (x^{2} - x) + 64 (y^{2} + 4 y) + 256 = 576

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{16} = 1

9 x^{2} + 25 y^{2} - 54 x - 100 y + 44 = 0

What is ((x-1)/2)^2+(y+3)^2= 49/64 ?
The solution to ((x-1)/2)^2+(y+3)^2= 49/64 is Ellipse with (h,k)=(1,-3),a= 7/4 ,b= 7/8