What is 5x^2-70x+9y^2+90y+425=0 ?

The solution to 5x^2-70x+9y^2+90y+425=0 is Ellipse with (h,k)=(7,-5),a=3,b=sqrt(5)

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5x^2-70x+9y^2+90y+425=0

5 x^{2} - 70 x + 9 y^{2} + 90 y + 425 = 0

(h, k) = (7, - 5), a = 3, b = 5

Solution steps

5 x^{2} - 70 x + 9 y^{2} + 90 y + 425 = 0

Rewrite

5 x^{2} - 70 x + 9 y^{2} + 90 y + 425 = 0

in the form of the standard ellipse equation

\frac{( x - 7 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (7, - 5), a = 3, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (7, - 5), a = 3, b = 5

(\frac{y - 3}{64})^{2} + \frac{( x + 5 ) ^{2}}{81} = 1

4 x^{2} + 9 y^{2} + 8 x + 18 y - 23 = 0

4 x^{2} + 9 y^{2} - 48 x + 72 y - 144 = 0

\frac{x ^{2}}{1 0 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

5 x^{2} + 20 x + 7 y^{2} + 14 y = 8

What is 5x^2-70x+9y^2+90y+425=0 ?
The solution to 5x^2-70x+9y^2+90y+425=0 is Ellipse with (h,k)=(7,-5),a=3,b=sqrt(5)