NCERT Class 11-Math՚S: Exemplar Chapter – 10 Straight Lines Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 6:

Show that the tangent of an angle between the lines is .

Answer:

Given:

And

Firstly, we find the slope of the given lines

Since, the above equation is in form.

So, Slope of the eq. (i) is

Now, finding the slope of the eq. (ii)

Since, the above equation is in form.

So, Slope of the eq. (ii) is

Let be the angle between the given two lines.

Putting the values of and in above eq. , we get

Hence, the required angle is

Hence Prove

Question 7:

Find the equation of lines passing through and making angle with y-axis.

Answer:

Question 8:

Find the equation of the line passing through the point of intersection of and and parallel to the line .

Answer:

Question 9:

For what values of a and b 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:

Question 10:

If the intercept of a line between the coordinate axes is divided by the point in the ratio , then find the equation of the line.

Answer:

Question 11:

Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of with the positive direction of axis.

[Hint: Use normal form, here .]

Answer:

Question 12:

Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by and the opposite vertex of the hypotenuse is .

Answer: