Question

question 7
which conic section is represented by $x^{2}+6y^{2}-7 = 0$
circle
ellipse
parabola
hyperbola

Explanation:

Step1: Recall general conic - section forms

The general second - degree equation is $Ax^{2}+Bxy + Cy^{2}+Dx + Ey+F = 0$. In the given equation $x^{2}+6y^{2}-7 = 0$, we have $A = 1$, $B = 0$, $C = 6$, $D = 0$, $E = 0$, $F=-7$.

Step2: Use the discriminant condition

The discriminant $\Delta=B^{2}-4AC$. Substituting the values, we get $\Delta = 0^{2}-4\times1\times6=- 24<0$. Also, $A
eq C$.

Step3: Identify the conic section

When $\Delta<0$ and $A
eq C$, the conic section is an ellipse.

Answer:

Ellipse