Question

Can someone explain how to solve these? Please.

http://gyazo.com/c40e767ad77b475c6caf987442f3012b

Answer 1

@AkashdeepDeb

Answer 2

You shouldn't JUST solve questions. Get to know the concepts first. It really helps. Learn about conic sections. KA has a really good series on it. Check it out first and then I'll help you! :D

https://www.khanacademy.org/math/algebra2/conics_precalc
http://www.stewartcalculus.com/data/BRIEF%20APPLIED%20CALCULUS/upfiles/ess-reviewofconics.pdf
http://www.sparknotes.com/math/precalc/conicsections/

Answer 3

compare
\(\large\tt \begin{align} \color{black}{x^2+8x+2y+24=0\\}\end{align}\)
with
\(\large\tt \begin{align} \color{black}{Ax^2+Bxy+Cy^2+Dx+Ey+F=0}\end{align}\)

\(\large\tt \begin{align} \color{black}{x^2+0xy+0y^2+8x+2y+24=0\\}\end{align}\)

\(\large\tt \begin{align} \color{black}{\triangle =B^2-4AC}\end{align}\)

here

\(\large\tt \begin{align} \color{black}{ \triangle =B^2-4AC\\
=0^2-4\times 1\times 0\\
=0}\end{align}\)

hence it is \(\Large parabola\)
use
\(\large\tt \begin{align} \color{black}{ \triangle =B^2-4AC=0 \implies parabola\\
\triangle =B^2-4AC\leq 0 \implies ellipse\\
\triangle =B^2-4AC\leq 0~~and~~A=C~~and~~B=0 \implies circle~~\\
\triangle =B^2-4AC\geq 0 \implies hyperbola
}\end{align}\)