Slope Intercept Form of a Line

Q.

If the lines represented by the equation $2x^2-3xy+y^2=0$ make angles $\alpha$ and $\beta$ with $x-$axis, then $co{t}^2\alpha +co{t}^2\beta$

1. $0$

2. $\frac{3}{2}$

3. $\frac{7}{4}$

4. $\frac{5}{4}$

Q.

The line which makes intercepts 3 and 4 on the x and the y axis respectively, has equation

1. 4x+3y=12

2. 3x-4y=12

3. 3x+4y=12

4. 4x-3y=12

Q. Find the equation of the straight line parallel to the line 3x+4y=7 and passing through the point { of intersection of the lines x-2y-3=0 and x+3y-6=0

Q.

The equation of the straight line which makes an angle of ${15}^{\circ }$ with the positive direction of x-axis and cuts an intercept of length 4 on the negative direction of y-axis, is

1. 

2. 

3. 

4. 

Q. 9. Find the equation of parabola whose focus -3, 2 and equation of directrix is x+y=4

Q. Show that the equation of the line passing through the origin and making an angle θ with the line .

Q. Find the equation of the line through the intersection of the lines 3x+4y=7 and x-4+2=0 and slope=5

Q. Find the equation of the line which intersects the y -axis at a distance of 2 units above the origin and makes an angle of 30° with the positive direction of the x -axis.

Q. Find the equation of a line drawn perpendicular to the line through the point, where it meets the y -axis.

Q. 27. let a line AB cuts of the intercept of 7 units and 7/3 units on the positive sides of axes find the number of integral values of m so that the X co-ordinate of the point of intersection of the lines mx+y=3 and AB is also an integer

Q.

Find the equation of a line passing through $(4,8)$ and equally inclined to the coordinate axes in the first quadrant.

Q.

The line 2x+3y=6, 2x+3y=8 cut the X-axis at a A, B respectively. A line L=o drawn through the point (2, 2) meets the X-axis at C in such a way that abscissae of A, B, C are in arithmetic progression. Then the equation of the line L is

1. 2x+3y=10

2. 3x+2y=10

3. 2x-3y=10

4. 3x-2y=10

Q.

A line cuts the x - axis at A(7, 0) and the y - axis at B(0, -5). A variable line PQ is drawn perpendicular to AB. Cutting the x - axis at P and the y - axis at Q.
If AQ and BP intersect at R, the locus of R is

1. $x^2+y^2+7x-5y=0$

2. $x^2+y^2-7x+5y=0$

3. 5x - 7y = 35

4. none of these

Q. The equation of the line whose slope is 3 and which cuts off an intercept 3 from the positive x - axis is

1. y=3x-9
2. y=3x+3
3. y=3x+9
4. None of these

Q. The equation of the line whose slope is 3 and which cuts off an intercept 3 from the positive x - axis is

1. y=3x-9
2. y=3x+3
3. y=3x+9
4. None of these

Q. If the lines y = 3 x + 1 and 2 y = x + 3 are equally inclined to the line y = mx + 4, find the value of m .

Q. The slope intercept form of the line $3x+7y+8=0$ is

1. $x=-\frac{7y}{3}-\frac{8}{3}$
2. $y=-\frac{3x}{7}+\frac{8}{7}$
3. $x=-\frac{7y}{3}+\frac{8}{3}$
4. $y=-\frac{3x}{7}-\frac{8}{7}$

Q. Find the equation of the line parallel to y -axis and drawn through the point of intersection of the lines x – 7 y + 5 = 0 and 3 x + y = 0.

Q. Represent to solution set of each of the following inequations graphically in two dimensional plane:

5. −3x + 2y ≤ 6

Q. Find the equation of the lines which cut off from the axes equal intercepts?

Q. The slope intercept form of the line $\frac{x}{2}+\frac{y}{4}=1$ is

1. $y=-2x+4$
2. $y=2x+4$
3. $y=4x+2$
4. $y=-4x+2$

Q.

Find the equation of the straight line passing through the point (-1, pi/2) and perpendicular to (3)^1/2sinA+2cosA=4/r.

Q. The equation of a straight line(s) passing through $(1,2)$ and having intercept of length $3$ units between the straight lines $3x+4y=24$ and $3x+4y=12$, is

1. $y=2$
2. $x=1$
3. $7x+24y+41=0$
4. $7x-24y+41=0$

Q. The line $L$ has intercepts $a$ and $b$ on the co-ordinate axes. When keeping the origin fixed, the co-ordinate axes are rotated through a fixed angle, then the same line has intercepts $p$ and $q$ on the rotated axes. Then

1. $\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{p^2}+\frac{1}{q^2}$
2. $a^2+p^2=b^2+q^2$
3. $a^2+b^2=p^2+q^2$
4. $\frac{1}{a^2}+\frac{1}{p^2}=\frac{1}{b^2}+\frac{1}{q^q}$

Q.

The equation of the straight line which makes an angle of ${15}^{\circ }$ with the positive direction of x-axis and cuts an intercept of length 4 on the negative direction of y-axis, is

1. $(2-\sqrt{3})x-y-4=0$

2. $(2-\sqrt{3})x+y-4=0$

3. $(2+\sqrt{3})x-y-4=0$

4. $(2+\sqrt{3})x-3y+7=0$

Q. 1. Find the co-ordinate of foot of perpendicular far the point (-1, 3) is the line 3x+4y-16=0

Q. Represent to solution set of each of the following inequations graphically in two dimensional plane:

6. x ≤ 8 − 4y

Q. 7. Find the distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x+2y=5 and x-3y=7