What is 9x^2+16y^2+42x-24y+57=0 ?

The solution to 9x^2+16y^2+42x-24y+57=0 is Ellipse with (h,k)=(-7/3 , 3/4),a= 1/3 ,b= 1/4

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9x^2+16y^2+42x-24y+57=0

9 x^{2} + 16 y^{2} + 42 x - 24 y + 57 = 0

(h, k) = (- \frac{7}{3}, \frac{3}{4}), a = \frac{1}{3}, b = \frac{1}{4}

Solution steps

9 x^{2} + 16 y^{2} + 42 x - 24 y + 57 = 0

Rewrite

9 x^{2} + 16 y^{2} + 42 x - 24 y + 57 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{7}{3} ) ) ^{2}}{( \frac{1}{3} ) ^{2}} + \frac{( y - \frac{3}{4} ) ^{2}}{( \frac{1}{4} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{7}{3}, \frac{3}{4}), a = \frac{1}{3}, b = \frac{1}{4}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{7}{3}, \frac{3}{4}), a = \frac{1}{3}, b = \frac{1}{4}

24 x^{2} + 9 y^{2} = 216

x^{2} + 4 y^{2} - 10 x + 16 y + 37 = 0

9 y^{2} = 36 - x^{2}

9 x^{2} + 5 y^{2} + 36 x - 30 y + 36 = 0

x, 4 x^{2} = 20 x - p (x)^{2} + 4

What is 9x^2+16y^2+42x-24y+57=0 ?
The solution to 9x^2+16y^2+42x-24y+57=0 is Ellipse with (h,k)=(-7/3 , 3/4),a= 1/3 ,b= 1/4