Parametric Form of a Straight Line

Q.

The equation of the pair of straight lines, each of which makes as angle $\alpha$ with the line y = x, is

1. 

2. 

3. 

4. 

Q.

Find the equation of a line which makes an angle of 135${}^{\circ }$ with the x-axis and passes through the point (3, 5)

Q.

Show that the equation of the line passing through the origin and making an angle $\theta$ with the line y = mx + c is $\frac{y}{x}=\frac{m\pm tan\theta }{1\mp mtan\theta }$

Q.

The tangent at any point P on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ with centre C,

meets the asymptotes in Q and R and cut off triangle CQR. Find the area of the triangle CQR.

1. \)

2. \)

3. 

4. ab

Q.

The middle point of the line segment joining (3, -1)and (1, 1) is shifted by two units (in the sense of increasing y) Perpendicular to the line segment. Then, the coordinates of the point in the new position are

1. 

2. 

3. 

4. 

Q. The line joining two points A (2, 0), B (3, 1) is rotated about A in anti - clockwise direction through an angle of ${15}^{\circ }$. Then the equation of the line in the new position if B goes to C in the new position, is

1. 
2. 
3. 
4. None of these

Q.

The equation $x^2-3xy+\lambda y^2+3x-5y+2=0$ When $\lambda$ is a real number, represents a pair of straight lines.If $\theta$ is the angle between the lines, then $cose{c}^2\theta =$ [EAMCET 1992]

1. 3

2. 9

3. 10

4. 100

Q. The parallelism condition for two straight lines one of which is specified by the equation ax+by+c=0 the other being represented parametrically by $x=\alpha t+\beta ,y=\gamma t+\delta$ is given by

1. $a\gamma =b\alpha =0$
2. $\alpha \gamma -b\alpha =0,\beta =\delta =c=0$
3. $a\alpha -b\gamma =0,\beta =\delta =0$
4. $a\alpha +b\gamma =0$

Q.

Find the direction in which a straight line must be drawn through the point (-1, 2) so that its point of intersection with the line x+y=4 may be at a distance of 3 units from this point.

Q.

For all values of $\theta$, the lines represented by the equation
$(2cos\theta +3sin\theta )x+(3cos\theta -5sin\theta )y-(5cos\theta -2sin\theta )=0$

1. pass through a fixed point

2. pass through the point (1, 1)

3. pass through a fixed point whose reflection in the line
   $x+y=\sqrt{2}$ is$(\sqrt{2}-1,\sqrt{2}-1)$

4. pass through the origin

Q. A plane passes through a fixed point $(p,q,r)$ and cuts the axes in A, B, C, Locus of the centre of the sphere OABC is

1. $\frac{p}{x}+\frac{q}{y}+\frac{r}{z}=1$

2. $\frac{p}{x}+\frac{q}{y}+\frac{r}{z}=2$

3. $\frac{x}{p}+\frac{y}{q}+\frac{z}{r}=1$

4. $\frac{x}{p}+\frac{y}{q}+\frac{z}{r}=2$

Q.

For all values of $\theta$, the lines represented by the equation
$(2cos\theta +3sin\theta )x+(3cos\theta -5sin\theta )y-(5cos\theta -2sin\theta )=0$

1. pass through a fixed point

2. pass through the point (1, 1)

3. pass through a fixed point whose reflection in the line
   $x+y=\sqrt{2}$ is$(\sqrt{2}-1,\sqrt{2}-1)$

4. pass through the origin