What is 49x^2+64y^2=25 ?

The solution to 49x^2+64y^2=25 is Ellipse with (h,k)=(0,0),a= 5/7 ,b= 5/8

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49x^2+64y^2=25

49 x^{2} + 64 y^{2} = 25

(h, k) = (0, 0), a = \frac{5}{7}, b = \frac{5}{8}

Solution steps

49 x^{2} + 64 y^{2} = 25

Rewrite

49 x^{2} + 64 y^{2} = 25

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{7} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{8} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{7}, b = \frac{5}{8}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{5}{7}, b = \frac{5}{8}

- 2 x^{2} - 8 x - y^{2} + 16 y = 52

9 x^{2} + 4 y^{2} - 90 x + 32 y + 145 = 0

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{16} = 1

\frac{( x + 3 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{9} = 1

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

What is 49x^2+64y^2=25 ?
The solution to 49x^2+64y^2=25 is Ellipse with (h,k)=(0,0),a= 5/7 ,b= 5/8