What is (2x-9)^2+(y)^2=5^2 ?

The solution to (2x-9)^2+(y)^2=5^2 is Ellipse with (h,k)=(9/2 ,0),a= 5/2 ,b=5

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(2x-9)^2+(y)^2=5^2

(2 x - 9)^{2} + (y)^{2} = 5^{2}

(h, k) = (\frac{9}{2}, 0), a = \frac{5}{2}, b = 5

Solution steps

(2 x - 9)^{2} + y^{2} = 5^{2}

Rewrite

(2 x - 9)^{2} + y^{2} = 5^{2}

in the form of the standard ellipse equation

\frac{( x - \frac{9}{2} ) ^{2}}{( \frac{5}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{9}{2}, 0), 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) = (\frac{9}{2}, 0), b = 5, a = \frac{5}{2}

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

25 x^{2} + 4 y^{2} - 100 = 0

x^{2} + 4 y^{2} = 46

9 x^{2} + y^{2} = 84

3 x^{2} + 2 y^{2} = 36

What is (2x-9)^2+(y)^2=5^2 ?
The solution to (2x-9)^2+(y)^2=5^2 is Ellipse with (h,k)=(9/2 ,0),a= 5/2 ,b=5