Distinguishing between Conics from General Equation and Eccentricity

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

1. Pair of lines
2. Ellipse
3. Parabola
4. Hyperbola

Q. The conic section represented by the equations $x=t^2+t+1$ and $y=t^2-t+1$ is ________ .

1. hyperbola
2. point
3. parabola
4. circle

Q. The locus represented by the equation $x^2+y^2-2x-2y+2=(2x+y-3{)}^2$ is

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

Q. Let $A(x_1,y_1)$ and $B(x_2,y_2)$ are two fixed points.Then locus of point $P$ such that

1. $\angle APB={90}^{\text{o}}$ is a circle
2. Area of $△APB$ is minimum is a parabola
3. $AP+PB=K$ where $K<AB$ is an ellipse
4. $\frac{AP}{PB}=K$ where $K<1$ is a circle

Q. The conic represented by the equation $13x^2-18xy+37y^2+2x+14y-2=0$ is

1. a parabola
2. a circle
3. an ellipse
4. a hyperbola

Q. If the equation $k{y}^2+y=x^2-16x+64$ represents a parabola then the value of $|4\Delta |=$

Q. The curve described parametrically by $x=\sin {}^{2}t,y=2\cos t$ represents

1. Hyperbola
2. Circle
3. Parabola
4. An elipse

Q. For the curve which is described parametrically by $x=t^2+t$ and $y=t^2-t$, the value of $|\Delta |$ is

Q. The conic represented by the equation $x^2+y^2-2xy+20x+10=0$ is

1. a parabola
2. an ellipse
3. a hyperbola
4. a pair fo straight line

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

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