What is ((x-h)^2)/(a^2)+((y-k)^2)/(b^2)=1 ?

The solution to ((x-h)^2)/(a^2)+((y-k)^2)/(b^2)=1 is Ellipse with (h,k)=(h,k),a=a,b=b

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((x-h)^2)/(a^2)+((y-k)^2)/(b^2)=1

\frac{( x - h ) ^{2}}{a ^{2}} + \frac{( y - k ) ^{2}}{b ^{2}} = 1

(h, k) = (h, k), a = a, b = b

Solution steps

\frac{( x - h ) ^{2}}{a ^{2}} + \frac{( y - k ) ^{2}}{b ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (h, k), a = a, b = b

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (h, k), a = a, b = b

x^{2} + y^{2} + 4 x - 6 y - 3 = 0

\frac{x ^{2}}{25} - \frac{y ^{2}}{4} = 1

9 x^{2} + 16 y^{2} = 144

y^{2} = - 25 x

\frac{x ^{2}}{4} - \frac{y ^{2}}{9} = 1

What is ((x-h)^2)/(a^2)+((y-k)^2)/(b^2)=1 ?
The solution to ((x-h)^2)/(a^2)+((y-k)^2)/(b^2)=1 is Ellipse with (h,k)=(h,k),a=a,b=b