Question

math chapter 10.3 class 11 ncrt questions

Answer 1

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Exercise 10.3

1. Reduce the following equations into slope-intercept form and find their slopes and the intercepts.

(i)

(ii)

(iii)

Ans. (i) Given:



……….(i)

Comparing with we have and

(ii) Given:



……….(i)

Comparing with we have and

(iii) Given:

……….(i)

Comparing with we have and

2. Reduce the following equations into intercept form and find their intercepts on the axis:

(i)

(ii)

(iii)

Ans. (i) Given:







Comparing with , we have and

(ii) Given:





Comparing with , we have and

(iii) Given:









Comparing with , we have and

3. Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular axis:

(i)

(ii)

(iii)

Ans. (i) Given:



Dividing both sides by we have





Putting and







=

Equation of line in normal form is

Comparing with we have and

(ii) Given:



Dividing both sides by we have

Putting and



Equation of line in normal form is

Comparing with we have and

(iii) Given:

Dividing both sides by we have





Putting and





Equation of line in normal form is

Comparing with we have and

4. Find the distance of the point from the line

Ans. Given: A line





Now, perpendicular distance of the point from the line is

= = = 5 units

5. Find the points on the axis, where distances from the line are 4 units.

Ans. Let the coordinates of the point on axis be

Now, perpendicular distance of the point from the line is

= =

According to question,



or

or

or

or

Therefore, the points on axis are (8, 0) and and

6. Find the distance between parallel lines:

(i) and

(ii) and

Ans. (i) Given: Two equations and

Here, and

Distance between two parallel lines =

= = = units

(ii) Given: Two equations and

Here, and

Distance between two parallel lines =

= = units

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

Ans. Given: Equation of a line which is parallel to the line is .

Since the line passes through point .







Therefore, the equation of required line is .

8. Find the equation of the line perpendicular to the line and having intercept 3.

Ans. Given: Equation of a line which is perpendicular to the line is .

Since the line passes through point .







Therefore, the equation of required line is .

9. Find the angles between the lines and

Ans. Given:





Also





Let be the angle between the lines.



= = =

and

and

10. The line through the points and (4, 1) intersects the line at right angle. Find the value of

Ans. Slope of the line passing through the points and (4, 1) =

Also slope of the line is

Since both lines are perpendicular to each other.

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