What is ((x^2-2x+1))/(34)+((y^2-8y+16))/(25)=1 ?

The solution to ((x^2-2x+1))/(34)+((y^2-8y+16))/(25)=1 is Ellipse with (h,k)=(1,4),a=sqrt(34),b=5

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((x^2-2x+1))/(34)+((y^2-8y+16))/(25)=1

\frac{( x ^{2} - 2 x + 1 )}{34} + \frac{( y ^{2} - 8 y + 16 )}{25} = 1

(h, k) = (1, 4), a = 34, b = 5

Solution steps

\frac{x ^{2} - 2 x + 1}{34} + \frac{y ^{2} - 8 y + 16}{25} = 1

Rewrite

\frac{x ^{2} - 2 x + 1}{34} + \frac{y ^{2} - 8 y + 16}{25} = 1

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 34 ) ^{2}} + \frac{( y - 4 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 4), a = 34, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 4), a = 34, b = 5

y^{2} \leq - 4 x^{2} + 4

\frac{( x - 4 ) ^{2}}{35} + \frac{( y - 2 ) ^{2}}{39} = 1

16 - 4 x^{2} - y^{2} > 0

\frac{( X - 7 ) ^{2}}{25} + \frac{( Y - 3 ) ^{2}}{16} = 1

12 x - 3 x^{2} + 36 y - 6 y^{2} > 0

What is ((x^2-2x+1))/(34)+((y^2-8y+16))/(25)=1 ?
The solution to ((x^2-2x+1))/(34)+((y^2-8y+16))/(25)=1 is Ellipse with (h,k)=(1,4),a=sqrt(34),b=5