The equation is 16x2+9y2−98x+5y+224=0

Question

hesgidiauE · Accepted Answer

All conic section can be written in the general form
$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$
The conic section represented by an equation in general form can be determine the coefficient.
If coefficient is $B^{2} - 4 A C < 0, B = 0 and A = C$ , then its equation of circle.
If coefficient is $B^{2} - 4 A C < 0, B \neq 0 or A \neq C$ , then its equation of ellipse
If coefficient is $B^{2} - 4 A C > 0$ , then its equation of hyperbola
If coefficicent is $B^{2} - 4 A C = 0$ , then its equation of ellipse
To find value of $B^{2} - 4 A C$
Compare general equation with given equation
Here $A = 16, B = 0, C = 9, D = - 98, E = 5 and F = 224$
$B^{2} - 4 A C = 0^{2} - 4 (16) (9) = - 576$
Here $B^{2} - 4 A C < 0, and A \neq C$
Therefore ,the given equation as an ellipse.

The equation is displaystyle{16}{x}^{2}+{9}{y}^{2}-{98}{x}+{5}{y}+{224}={0}

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