What is x^2+4y^2+10x+9y-7=0 ?

The solution to x^2+4y^2+10x+9y-7=0 is Ellipse with (h,k)=(-5,-9/8),a=(sqrt(593))/4 ,b=(sqrt(593))/8

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x^2+4y^2+10x+9y-7=0

x^{2} + 4 y^{2} + 10 x + 9 y - 7 = 0

(h, k) = (- 5, - \frac{9}{8}), a = \frac{593}{4}, b = \frac{593}{8}

Solution steps

x^{2} + 4 y^{2} + 10 x + 9 y - 7 = 0

Rewrite

x^{2} + 4 y^{2} + 10 x + 9 y - 7 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{( \frac{593}{4} ) ^{2}} + \frac{( y - ( - \frac{9}{8} ) ) ^{2}}{( \frac{593}{8} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, - \frac{9}{8}), a = \frac{593}{4}, b = \frac{593}{8}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, - \frac{9}{8}), a = \frac{593}{4}, b = \frac{593}{8}

16 x^{2} + 9 y^{2} - 32 x + 90 y + 145 = 0

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

\frac{( x - 2 ) ^{2}}{64} + \frac{( y - 4 ) ^{2}}{16} = 1

\frac{( x + 3 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

5 x^{2} + 9 y^{2} = 100

What is x^2+4y^2+10x+9y-7=0 ?
The solution to x^2+4y^2+10x+9y-7=0 is Ellipse with (h,k)=(-5,-9/8),a=(sqrt(593))/4 ,b=(sqrt(593))/8