What is 7x^2+16y^2-14x-64y-41=0 ?

The solution to 7x^2+16y^2-14x-64y-41=0 is Ellipse with (h,k)=(1,2),a=4,b=sqrt(7)

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7x^2+16y^2-14x-64y-41=0

7 x^{2} + 16 y^{2} - 14 x - 64 y - 41 = 0

(h, k) = (1, 2), a = 4, b = 7

Solution steps

7 x^{2} + 16 y^{2} - 14 x - 64 y - 41 = 0

Rewrite

7 x^{2} + 16 y^{2} - 14 x - 64 y - 41 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 4, b = 7

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 2), a = 4, b = 7

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

4 x^{(2)} + 9 y^{(2)} = 36

\frac{( x - 2 ) ^{2}}{36} + \frac{( y - 6 ) ^{2}}{4} = 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{81} = 1

4 y^{2} + 3 x^{2} = 48

What is 7x^2+16y^2-14x-64y-41=0 ?
The solution to 7x^2+16y^2-14x-64y-41=0 is Ellipse with (h,k)=(1,2),a=4,b=sqrt(7)