Family of straight lines

Q.

The equation of the bisectors of angle between the lines represented by equation $(y-mx{)}^2=(x+my{)}^2$ is

1. 

2. 

3. 

4. None of these

Q.

Let $z_1,z_2,z_3$ are the vertices of an equilateral triangle inscribed in the circle $\left|z\right|$ = 2. If $z_1,z_2,z_3$ are in the clockwise sense and $z_1$ = $1+i\sqrt{3}$, then:

1. = , = -2

2. = , = 2

3. = , = 2

4. =

Q.

The equation of the diameter of the circle $x^2+y^2+2x-4y-11=0$ which bisects the chords intercepted on the line $2x-y+3=0$ is

1. 

2. 

3. 

4. x+2y+3=0

Q.

If a circle and rectangular hyperbola $xy=c^2$ meet in the four points $t_1,t_2,t_3\&t_4$ . Then which of the following statements are correct?
1. The center of the mean position of the four points bisects the distance between the center of the two curve.
2. Center of the circle through the points $t_1,t_2\&t_3$ is:$\left[\right(\frac{c}{2}(t_1+t_2+t_3)+\frac{1}{t_1.t_2.t_3}),\frac{c}{2}(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+t_1{t}_2{t}_3\left)\right]$

1. Only 1

2. Only 2

3. Both 1 & 2

4. None of these

Q.

A visitor with sign board 'DO NOT LITTER' is moving on a circular path in an exhibition. During the movement, he stops at points represented by (3, -2) and (-2, 0). Also, centre of the circular path is on the line 2x - y = 3. What is the equation of the path? What message he wants to give in the public domain?

Q.

10 students are participating in a debate on 'SAVE WILD LIFE'. Five students have to speak in favour and five students against it. These students are standing on two lines face-to-face whose equations are 3x - y - 4 = 0 and 6x - 2y -4 = 0 for a debate. Are the students standing on parallel lines ?

During the debate, which team you are in favour of? Why?

Q.

Find the equations of tangents to the ellipse
$\frac{x^2}{25}+\frac{y^2}{16}=1$
which are parallel to $3x+2y=25$

1. $3x+2y=17$

2. $3x+2y+17=0$

3. $3x+2y+32=0$

4. $3x+2y=32$

Q.

Find the equation of normal having slope 1 to the parabola
$y^2=4x$

1. $y=x-3$

2. $y=x+3$

3. $y=x$

4. $y=2x-3$

Q.

If y = mx be one of the bisectors of the angle between the lines $a{x}^2-2hxy+b{y}^2=0$, then

1. $h(1-m^2)+m(a-b)=0$

2. $h(1-m^2)+m(a+b)=0$

3. $h(1-m^2)+m(a-b)=0$

4. $h(1+m^2)+m(a+b)=0$

Q.

The circle $x^2+y^2=1$ cuts the x-axis at P and Q. Another circle with centre at Q and variable radius intersects to first circle at R above the X-axis and the line segment PQ at S. The maximum area of the triangle QSR is

1. 

2. 

3. 

4. 

Q.

The point of intersection of the tangents of the circle $x^2+y^2=10$, drawn at end points of the chord x + y = 2 is

1. (–5, –5)

2. (–5, –4)

3. (–4, –5)

4. None of these

Q.

What is the point-slope form of a line that has a slope of $3$ and passes through the point $\left(-1,4\right)$?

1. $y-\left(-1\right)=5\left(x-4\right)$

2. $4-y_1=3\left(-1-x_1\right)$

3. $y-3=-1\left[\left(x-\left(-4\right)\right)\right]$

4. $y-4=3\left[\left(x-\left(-1\right)\right)\right]$

Q.

Match the following. Graph of f(x) is given

1. 

2. 

3. 

4. 

Q. Without using the Pythagoras theorem, show that the points $(4,4),(3,5)$ and $(1,1)$ are the vertices of a right angled triangle

Q. A circle passes through the points A(1, 0), B(5, 0) and C(0, h). If \(\angle ACB\) is maximum then

1. 
2. 
3. 
4. 

Q.

If two of the lines given by $3x^3+3x^{2}y-3x{y}^2+d{y}^3=0$ are at right angles then the slope of one of them is

1. -1

2. 1

3. 3

4. -3

Q. Locus of the image of the point (2, 3) in the line $(2x-3y+4)+k(x-2y+3)=0,kϵR,$ is a

1. Straight line parallel to y-axis
2. Straight line parallel to x-axis
3. Circle of radius $\sqrt{2}$
4. Circle of adius 3

Q. Locus of the image of the point (2, 3) in the line $(2x-3y+4)+k(x-2y+3)=0,kϵR,$ is a

1. Straight line parallel to y-axis
2. Circle of adius 3
3. Straight line parallel to x-axis
4. Circle of radius $\sqrt{2}$

Q.

The combined equation of the asymptotes for the hyperbola $x^2-2y^2=2$

1. 

2. 

3. 

4. 

Q.

Equation of the straight line passing through the point of intersection of the lines $3x+4y=7,x-y+2=0$ and having slope $3$ is

1. 21x−7y+16=0

2. 9x−3y+14=0

3. 21x−7y+12=0

4. 9x−3y+5=0

Q.

Find the equation of lines passing through intersection of lines x+y+4 = 0 and 3x-y-8 = 0 and equally inclined to axis..

1. x-y-6 = 0

2. x+y+4 = 0

3. x+y+6 = 0

4. 3x-y-8 = 0

Q.

Find the equation of straight line which passes through the point (2, -3) and the point of intersection of the lines x+y +4 = 0 and 3x-y-8=0

1. x-2y-7 = 0

2. 2x-y-7 = 0

3. x-2y+7 = 0

4. 2x-y+7 = 0

Q.

If a and b are two arbitrary constants, then the straight line (a-2b)x + (a+3b)y + 3a+4b = 0 will pass through

1. (-1, -2)

2. (1, 2)

3. (-2, -3)

4. (2, 3)

Q. Let a and b be non-zero and real numbers. Then, the equation
$(a{x}^2+b{y}^2+c)(x^2-5xy+6y^2)=0$ represents

1. Four straight lines, when c=0 and a, b are of the same sign
2. Two straight lines and a circle, when a=b and c is of sign opposite to that of a
3. Two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a
4. A circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a