Distinguishing between Conics from General Equation and Eccentricity

Q. The value(s) of $k$ if the equation $9x^2+4y^2+2kxy+4x-2y+3=0$ represents a parabola, is (are)

1. $6$
2. $36$
3. $-6$
4. $-36$

Q. The curve described parametrically by $x=3\cos \left(2t\right),y=1+{\cos }^2\left(2t\right)$ represents

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

Q. If $2x^2+7xy+3y^2+8x+14y+k=0$ represents a pair of straight lines, then the value of $k$ is

1. $5$
2. $18$
3. $8$
4. $16$

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 pair of straight lines
4. a hyperbola

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

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

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 curve represented by the equation $xy=1$ represents

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

Q. If $2x^2+7xy+3y^2+8x+14y+k=0$ represents a pair of straight lines, then the value of $k$ is

1. $5$
2. $18$
3. $8$
4. $16$

Q. The equation $13x^2-18xy+37y^2+2x+14y-2=0$ represents

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

Q. The curve represented by the parameters $x=t^2+1$ and $y=2t+1$ is

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

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 locus of a point (to the right of $x=2$) whose sum of the distances from the origin and the line $x=2$ is $4$ units, is

1. $y^2=-12(x-3)$
2. $y^2=12(x-3)$
3. $x^2=12(y-3)$
4. $x^2=-12(y-3)$

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 curve represented by the equation $xy=1$ represents

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

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

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

Q. The curve described parametrically by $y=2at$ and $x=a{t}^2,$ where $\alpha$ is a non-zero constant, represents

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

Q. The curve described parametrically by $x=t^2+t,y=2t-1$ represents

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

Q. If the parabola $x^2=ay$ makes an intercept of length $\sqrt{40}$ units on the line $y-2x=1$, then $a$ is equal to

1. $1$
2. $-2$
3. $-1$
4. $2$