# NCERT Class 11-Math՚S: Exemplar Chapter – 10 Straight Lines Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Long Answer Type

**Question 13**:

If the equation of the base of an equilateral triangle is and the vertex is , then find the length of the side of the triangle.

[**Hint**: Find length of perpendicular from to the line and use , where is the length of side of the triangle] .

**Answer**:

**Question 14**:

A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points and on the line is zero. Find the coordinates of the point P.

[**Hint**: Let the slope of the line be *m*. Then the equation of the line passing through the fixed point is . Taking the algebraic sum of perpendicular distances equal to zero, we get . Thus .]

**Answer**:

**Question 15**:

In what direction should a line be drawn through the point so that its point of intersection with the line is at a distance from the given point.

**Answer**:

**Question 16**:

A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.

line passes through the fixed point (k, k) .

**Answer**:

Intercepts form of a straight line is

Where a and b are the intercepts on the axes

Given that:

This shows that the line is passing through the fixed point

**Question 17**:

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**:

**Question 18**:

Find the equations of the lines through the point of intersection of the lines and and whose distance from the point is .

**Answer**:

and

**Question 19**:

If the sum of the distances of a moving point in a plane from the axes is , then find the locus of the point.

[**Hint**: Given that , which gives four sides of a square.]

**Answer**:

Let the coordinates of a moving point P be

Given that the sum of the distance from the axes to the point is always

Hence, these equations gives us the locus of the point P which is a square.

**Question 20**:

are points on either of the two lines at a distance of units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from on the bisector of the angle between the given lines.

[**Hint**: Lines are and according as or . *y*-axis is the bisector of the angles between the lines. P1, P2 are the points on these lines at a distance of 5 units from the point of intersection of these lines which have a point on *y*-axis as common foot of perpendiculars from these points. The *y*-coordinate of the foot of the perpendicular is given by 2 + 5 cos30°.]

**Answer**: