General Equation of Conics

Q. The conic represented by the equation $x^2+y^2+2xy+4x-6y+17=0$ is

1. a hyperbola
2. a parabola
3. a pair of straight lines
4. an ellipse

Q.

The equation of directrix of a conic is
$L:x+y-1=0$ and the focus is the point $(0,0)$. Find the equation of the conic if its eccentricity is
$\frac{1}{\sqrt{2}}$

1. $3x^2+3y^2+2xy+2x+2y-1=0$

2. $3x^2+3y^2+2xy+2x+2y+1=0$

3. $3x^2+3y^2+2xy-2x-2y+1=0$

4. $3x^2-3y^2+2xy+2x-2y+1=0$

Q. The locus of the point of intersection of the lines $\left(\sqrt{3}\right)kx+ky-4\sqrt{3}=0$ and $\sqrt{3}x–y–4\left(\sqrt{3}\right)k=0$ is a conic, whose eccentricity is

Q.

Dilate the figure using the indicated scale factor $\mathrm{k}$. What is the value of the ratio (new to original) of the perimeters? The areas? a square with vertices $(0,0),(0,4),(4,4)$ and $(4,0);\mathrm{k}=0.5$.