Distinguishing between Conics from General Equation and Eccentricity

Q.

The values of $h$ for which the equation $3x^2+2hxy-3y^2-40x+30y-75=0$ represents a pair of straight lines, are

1. $4,4$

2. $4,6$

3. $4,-4$

4. $0,4$

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.

Which of the following second-degree equation represents a pair of straight lines?

1. ${\mathrm{x}}^2–\mathrm{xy}–{\mathrm{y}}^2=1$

2. $–{\mathrm{x}}^2+\mathrm{xy}–{\mathrm{y}}^2=1$

3. $4{\mathrm{x}}^2–4\mathrm{xy}+{\mathrm{y}}^2=4$

4. ${\mathrm{x}}^2+{\mathrm{y}}^2=4$

Q. The curve represented by the equation $xy=1$ represents

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

Q.

The number of different straight lines that are formed with A (2, 3), B(3, 4), C(5, 6), D(3, 7) are

1. 1

2. 0

3. 3

4. 4

Q.

The locus of a point which divides the join of A(-1, 1) and a variable point P on the circle $x^2+y^2=4$ in the ratio 3:2, is

1. 

2. 

3. 

4. 

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. Let A, B and C be the sets such that A union B is equal to A union C and A intersection B is equal to A intersection C. show that B is equal to C

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. 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. 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. $2$

Q.

Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.

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. The curve described parametrically by $x=2(\cos t+\sin t),y=5(\cos t-\sin t)$ represents

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

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

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. The equation $12x^2-23xy+10y^2-25x+26y-14=0$ represents

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

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

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 number of different hyperbolas represented by the equation ${(}^m{C}_n{)}^2(x+y+1{)}^2=2\left\{\right(x-3{)}^2+(y-4{)}^2\}$ with $1\le n<m\le 5$ is ___

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. 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 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. If the equation $2xy+4x-6y+k=0$ represents a pair of straight lines, then the value of $(k+20)$ is

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

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 $y^2-4x-4y+\lambda =0$

1. A parabola $\forall \lambda \in R$
2. $e=1$ when $\lambda =2020$
3. an ellipse if $\lambda <0$
4. A non-degenerate conic

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

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

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

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