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

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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] .

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 .]

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.

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) .

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.

Question 18:

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

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.]

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°.]