What is 4x^2+25y^2+8x=96 ?

The solution to 4x^2+25y^2+8x=96 is Ellipse with (h,k)=(-1,0),a=5,b=2

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4x^2+25y^2+8x=96

4 x^{2} + 25 y^{2} + 8 x = 96

(h, k) = (- 1, 0), a = 5, b = 2

Solution steps

4 x^{2} + 25 y^{2} + 8 x = 96

Rewrite

4 x^{2} + 25 y^{2} + 8 x = 96

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), a = 5, b = 2

(\frac{x ^{2}}{16}) + (\frac{y ^{2}}{25}) = 1

\frac{( x + 4 ) ^{2}}{6 ^{2}} + \frac{( y + 6 ) ^{2}}{7 ^{2}} = 1

X^{2} + 4 Y^{2} - 6 X - 16 Y + 21 = 0

(5 p + 3 q) 2 = 25 p^{2} + 9 q^{2}

25 x^{2} + 9 y^{2} + 100 x + 36 y - 89 = 0

What is 4x^2+25y^2+8x=96 ?
The solution to 4x^2+25y^2+8x=96 is Ellipse with (h,k)=(-1,0),a=5,b=2