Identify the conic section represented by 5x^2-7x+2y^2=10. Explain.

Question

anonymous · Answer

Why don't you use discriminant test?

directrix · Answer

It looks as if it may be an ellipse. To be sure and to explain why, you will need to write the equation in that of standard form for an ellipse. See that form at the link: http://tutorial.math.lamar.edu/Classes/Alg/Ellipses.aspx

anonymous · Answer

A quadratic equation of the form $Ax^2+Bxy+Cy^2 +Dx+Ey+F=0$ is an ellipse if $B^2-4AC \lt 0 $

Here we have $ 5x^2-7x+2y^2=10 $

A = 5
C= 2
B = 0

So,$ 0^2 - 4 (5) (2) \lt 0 \implies $ Ellipse.

anonymous · Answer

There are even short cut for this, but I am not sure if it is applicable in rigorous/analytic mathematics.