1.2 – N – CONICS Exercise Problems

\[\underline{PART\ -\ A}\]
\[1.\ Define\ Conic\ \hspace{18cm}\]
\[2.\ Prove\ that\ the\ equation\ x^2\ -\ 2\ x\ y\ +\ y^2\ -\ 16\ x\ -\ 12\ y\ +\ 22\ = 0\ is\ a\ parabola\ \hspace{5cm}\]
\[3.\ Show\ that\ the\ equation\ 7\ x^2\ +\ 3\ x\ y\ +\ 2\ y^2\ -\ x\ +\ 2\ y\ -\ 1\ = 0\ represents\ an\ ellipse\ \hspace{5cm}\]
\[\underline{PART\ -\ B}\]
\[4.\ Show\ that\ the\ equation\ 4\ x^2\ +\; 10\ x\ y\ +\ y^2\ -\ 2\ x\ +\ 5\ y\ -\ 3\ = 0\ represents\ a\ hyperbola\ \hspace{5cm}\]
\[5.\ Find\ the\ equation\ of\ the\ parabola\ with\ its\ focus\ at\ (-1,\ -2)\ and\ x\ +\ 2\ y\ =\ 0\ as\ its\ directrix\ \hspace{5cm}\]
\[\underline{PART\ -\ C}\]
\[6.\ Prove\ that\ equation\ 2\ x^2\ -\ 7\ x\ y\ +\ 3\ y^2\ +\ 5\ x\ -\ 5\ y\ +\ 2\ =\ 0\ \hspace{7cm}\]\[represents\ a\ pair\ of\ straight\ lines\ \hspace{5cm}\]
\[7.\ Prove\ that\ equation\ 3\ x^2\ +\ 7\ x\ y\ +\ 2\ y^2\ +\ 5\ x\ +\ 5\ y\ +\ 2\ =\ 0\ \hspace{7cm}\]\[represents\ a\ pair\ of\ straight\ lines\ \hspace{5cm}\]
\[8.\ For\ the\ quadratic\ equation\ 2\ x^2\ +\ 7\ x\ y\ +\ 3\ y^2\ +\ 13\ x\ -\ \ y\ -\ 24\ =\ 0\ \hspace{7cm}\]\[identify\ the\ conic\ \hspace{5cm}\]