General Equation of a Conic

Q.

Find the asymptotes of hyperbola xy - 3y - 2x = 0

1. x = 3

2. x = 2

3. y = 2

4. y = 3

Q. The equation of the circle whose centre is (1, -3) and which touches the line 2x - y - 4 = 0 is

1. None of these
2. 
3. 
4. 

Q.

The mid-point of the chord 4x - 3y = 5 of the hyperbola $2x^2-3y^2=12$ is

1. \)

2. \)

3. \)

4. \)

Q.

Equation of the hyperbola with focus (-3, 4) directrix 3x-4y+5=0 and e = $\frac{5}{2}$ is

1. $5x^2-24xy+12y^2+6x-8y-75=0$

2. $5x^2-24xy+12y^2-8x-6y-25=0$

3. $5x^2-24xy+12y^2-12x+8y-55=0$

4. $5x^2-24xy+12y^2-7x-12y-65=0$

Q.

The angle between the pair of straight lines $x^2-y^2-2y-1=0$, is

1. 

2. 

3. 

4. 

Q.

Find the asymptotes of the hyperbola xy - 3y - 2x = 0

1. x = 3

2. x = 2

3. y = 2

4. y = 3

Q.

A chord of contact of a point P(k, 2k) is drawn with respect to the circle $x^2+y^2+2x+2y-9=0$. What is the value of 'k' if the chord passes through the origin?

1. -1

2. 

3. 3

4. -5

Q.

Match the column

$\begin{array}{cc}\text{Equation}& \text{Name of the curve}\\ \text{1)}{x}^2-2x-y-3=0& \text{P) Circle}\\ \text{2)}{x}^2+3xy+2y^2-x-4y-6=0& \text{Q) Parabola}\\ \text{3)}{x}^2+y^2-20=0& \text{R) Ellipse}\\ \text{4)}7x^2+7y^2+2xy+10x-10y+7=0& \text{S) Hyperbola}\\ \text{5)}6x^2-xy-y^2-23x+4y+15=0& \text{T) Pair of straight lines}\end{array}$

1. 1 - T, 2 - Q, 3 - P, 4 - R, 5 - S

2. 1 - Q, 2 - T, 3 - P, 4 - R, 5 - S

3. 1 - Q, 2 - T, 3 - P, 4 - S, 5 - R

4. 1 - Q, 2 - S, 3 - P, 4 - T, 5 - R

Q. Match the following equations with corresponding conic:

1. Circle
2. Straight Line
3. Parabola

Q. If sum of the perpendicular distances of a variable point $P(x,y)$ from the lines $x+y-5$ $=$ $0$ and $3x-2y+7$ $=$ $0$ is always $10$. Show that $P$ must move on a line.

Q.

What is the equation of the chord centered at (1, 2) in the circle $x^2+y^2-4x-6y-10=0$

1. $x-y-3=0$

2. $x-y+3=0$

3. $x+y-3=0$

4. $x+y+3=0$

Q.

Find the equations of the medians of a \(\triangle\) ABC whose vertices are A(2, 5), B(-4, 9) and C(-2, -1).