*Note: We know that the equation of the line is where is the x-intercept and is the y-intercept.*

Question 1: Find the equation to the straight line:

(i) cutting off intercepts and from the axes.

(ii) cutting off intercepts and from the axes.

Answer:

i) Here

Therefore the equation of the line:

ii) Here

Therefore the equation of the line:

Question 2: Find the equation of the straight line which passes through and cuts off equal intercepts on the axes.

Answer:

Here

Therefore the equation of the line:

Since the line passes through we get

Hence the equation of the line is

Question 3: Find the equation to the straight line which, passes through the point and has intercepts on the axes (i) equal in magnitude and both positive. (ii) equal in magnitude but opposite in sign.

Answer:

i) Here

Therefore the equation of the line:

Since the line passes through we get

Hence the equation of the line is

ii) Here

Therefore the equation of the line:

Since the line passes through we get

Hence the equation of the line is

Question 4: For what values of and the -intercepts cut off on the coordinate axes by the line are equal in length but opposite in signs to those cut off by the line on the axes.

Answer:

Given

Therefore the x-intercept and y-intercept

We also have

Therefore the x-intercept and y-intercept

and

Question 5: Find the equation to the straight line which cuts off equal positive intercepts on the axes and their product is .

Answer:

Here

Solving:

Since the intercepts are positive, we get

Therefore the equation of the line:

Question 6: Find the equation of the line which passes through the point and the portion of the line intercepted between the axes is divided internally in the ratio by this point.

Answer:

Let the intercepts be and .

Given divides the and in the ratio of

Similarly

Since the equation of line passing through , therefore

Question 7: A straight line passes through the point and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight ling is .

Answer:

Let the intercepts be and .

Given divides the and in the ratio of

Similarly

Hence the equation of line is:

. Hence proved.

Question 8: Find the equation of the line which passes through the point and is such that the portion of it intercepted between the axes is divided by the point in the ratio .

Answer:

Let the intercepts be and .

Given divides the and in the ratio of

i.e.

Similarly

Since the equation of line passing through , therefore

Question 9: Point divides a line segment between the axes in the ratio . Find the equation of the line.

Answer:

Let the intercepts be and .

Given divides the and in the ratio of

i.e.

Similarly

Since the equation of line passing through , therefore

Question 10: Find the equation of the straight line which passes through the point and cuts off positive intercepts on the coordinate axes whose sum is .

Answer:

Let the intercepts be and .

Given: .

The line also passes through . Therefore

Since the intercepts are positive we get

Hence the equation of the line is:

Question 11: Find the equation to the straight line which passes through the point and is such that the portion of it between the axes is divided by the point in the ratio .

Answer:

Let the intercepts be and .

Given divides the and in the ratio of

Similarly

Since the equation of line passing through , therefore

Question 12: Find the equation of a line which passes through the point and is such that the intercept on x-axis exceeds the intercept on y-axis by .

Answer:

Let the intercepts be and .

Given:

The line also passes through . Therefore

Hence the equation of the lines are:

or

or

Question 13: Find the equation of the line, which passes through and meets the axes at and respectively so that .

Answer:

Let the intercepts be and .

Given

Given divides the and in the ratio of

Similarly

Since the equation of line passing through , therefore

Question 14: Find the equation of the line passing through the point and cutting off intercepts on the axes whose sum is .

Answer:

Let the intercepts be and .

Given:

The line also passes through . Therefore

Hence the equation of the lines are:

or

or

Question 15: Find the equation of the straight line which passes through the point and cuts the coordinate axes at the point and respectively so that .

Answer:

Let the intercepts be and .

Given

Given divides the and in the ratio of

Similarly

Since the equation of line passing through , therefore

Question 16: Find the equations of the straight lines each of which passes through the point and cuts off intercepts and respectively on x and y-axes such that .

Answer:

Let the intercepts be and .

Given:

The line also passes through . Therefore

Hence the equation of the lines are:

or

or

Question 17: Find the equations of the straight lines which pass through the origin and trisect the portion of the straight line which is intercepted between the axes.

Answer:

Given line

x-intercept

y-intercept

divides in the ratio of

Coordinates of

divides in the ratio of

Coordinates of

Slope of

Therefore equation of :

Slope of

Similarly, equation of :

Question 18: Find the equation of the straight line passing through the point and bisecting the portion of the straight line lying between the axes.

Answer:

Given

Therefore intercepts of and axis are and

Mid point of

Slope of line passing through M and ( 2, 1)

Therefore equation of :

Question 19: Find the equation of the straight tine passing through the origin and bisecting the portion of the line intercepted between the coordinate axes.

Answer:

Given

When y-intercept

When y-intercept

Therefore midpoint of

Slope of

Similarly, equation of :