What is (x-5)^2+(y+8)^2+(x-3)^2-98=0 ?

The solution to (x-5)^2+(y+8)^2+(x-3)^2-98=0 is Ellipse with (h,k)=(4,-8),a=4sqrt(3),b=4sqrt(6)

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(x-5)^2+(y+8)^2+(x-3)^2-98=0

(x - 5)^{2} + (y + 8)^{2} + (x - 3)^{2} - 98 = 0

(h, k) = (4, - 8), a = 43, b = 46

Solution steps

(x - 5)^{2} + (y + 8)^{2} + (x - 3)^{2} - 98 = 0

Rewrite

(x - 5)^{2} + (y + 8)^{2} + (x - 3)^{2} - 98 = 0

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( 4 3 ) ^{2}} + \frac{( y - ( - 8 ) ) ^{2}}{( 4 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 8), a = 43, b = 46

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 8), b = 46, a = 43

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

4 x^{2} + 7 y^{2} = 28

5 u^{2} - 4 \cdot u + v^{2} + 2 \cdot v = 0

3 x^{2} + 2 y^{2} - 6 x - 12 y + 15 = 0

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

What is (x-5)^2+(y+8)^2+(x-3)^2-98=0 ?
The solution to (x-5)^2+(y+8)^2+(x-3)^2-98=0 is Ellipse with (h,k)=(4,-8),a=4sqrt(3),b=4sqrt(6)