What is y^2=9+(-(5x+4)(5x-6))/2 ?

The solution to y^2=9+(-(5x+4)(5x-6))/2 is Ellipse with (h,k)=(1/5 ,0),a=(sqrt(43))/5 ,b=sqrt(43/2)

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y^2=9+(-(5x+4)(5x-6))/2

y^{2} = 9 + \frac{- ( 5 x + 4 ) ( 5 x - 6 )}{2}

(h, k) = (\frac{1}{5}, 0), a = \frac{43}{5}, b = \frac{43}{2}

Solution steps

y^{2} = 9 + \frac{- ( 5 x + 4 ) ( 5 x - 6 )}{2}

Rewrite

y^{2} - 9 - \frac{- ( 5 x + 4 ) ( 5 x - 6 )}{2} = 0

in the form of the standard ellipse equation

\frac{( x - \frac{1}{5} ) ^{2}}{( \frac{43}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{43}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{5}, 0), a = \frac{43}{5}, b = \frac{43}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{5}, 0), b = \frac{43}{2}, a = \frac{43}{5}

x^{2} + 4 y^{2} - 6 x + 16 y = - 9

4 x^{2} + y^{2} + 2 y - 15 = 0

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

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

What is y^2=9+(-(5x+4)(5x-6))/2 ?
The solution to y^2=9+(-(5x+4)(5x-6))/2 is Ellipse with (h,k)=(1/5 ,0),a=(sqrt(43))/5 ,b=sqrt(43/2)