Intercept of a Straight Line

Q.

The equation of the directrices of the ellipse $16x^2+25y^2=400$ are

1. 

2. 

3. 

4. 

Q.

A straight line meet the axes in A and B such that the centroid of triangle OAB is (a, a). Then the equation of the line AB is

1. x+y=a

2. x−y=3a

3. x+y=2a

4. x+y=3a

Q.

P(a, b) is the mid point of a line segmen between axis. Show that equation of the line is $\frac{x}{a}+\frac{y}{b}=2$

Q.

The equation of the line which cuts off an intercept $3\mathrm{units}$ on $OX$and an intercept $-2\mathrm{unit}$ on $OY$, is

1. $\frac{x}{3}-\frac{y}{2}=1$

2. $\frac{x}{3}+\frac{y}{2}=1$

3. $\frac{x}{2}+\frac{y}{3}=1$

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

Q.

Solve the following system of inequation graphically.

$x+2y\le 8,x+y\ge 4,x-y\ge 0,y\ge 0$

Name the common region and write down its vertices

Q.

Find the equation of a line that cuts off equal intercepts on the cordinate axis and passes through the point (2, 3).

Q. The area of triangle formed by the lines x = 0, y = 0 and $\frac{x}{a}+\frac{y}{b}=1$, a and b are positive , is

1. 
2. 
3. 
4. 

Q.

A line passes through P(1, 2) such that its intercept between the axes is bisected at P. Find the equation of line.

Q.

Find the equation of line parallel to the y- axis and drawn through the point of intersection of $x-7y=-5and3x+y-7=0.$

Q. The area enclosed by $2|x|+3|y|\le 6$ is

1. $3$ sq. units
2. $4$ sq. units
3. $12$ sq. units
4. $24$ sq. units

Q. The equation of the straight line which passes through the point (1, - 2) and cuts off equal intercepts from axes, is

1. x+y=1
2. x-y=1
3. x+y+1=0
4. x-y-2=0

Q. The area of triangle formed by the lines x = 0, y = 0 and $\frac{x}{a}+\frac{y}{b}=1$, a and b are positive , is

1. $ab$
2. $\frac{ab}{2}$
3. $2ab$
4. $\frac{ab}{3}$

Q. The equation of the straight line which passes through the point $P(-4,3)$ such that the portion of it between the $x$-axis and $y$-axis is divided by the point $P$ in the ratio $1:2$ respectively, is

1. $\frac{x}{6}-\frac{y}{9}=1$
2. $\frac{x}{9}-\frac{y}{6}=1$
3. $\frac{y}{9}-\frac{x}{6}=1$
4. $\frac{y}{9}+\frac{x}{6}=1$