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NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines
NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines Ex 10.3 are part of NCERT Solutions for Class 11 Maths. Here we have given Class 11 Maths NCERT Solutions Straight Lines Ch 10 Exercise 10.3.
Maths NCERT Solutions Class 11 Maths Chapter 10 Exercise.10.3
Q1. Reduce the following equations into slope-intercept form and find their slopes and the y intercepts.
(i) x + 6y = 0
(ii) 6x + 3y – 6 = 0
(iii) y = 1
Q2. Reduce the following equations into intercept form and find their intercepts on the axes.
(i) 3x + 2y – 14 = 0
(ii) 4x – 3y = 6
(iii) 3y + 2 = 0
Q3. Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.
(ii) y – 2 = 0
(iii) x – y = 4
Q4. Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).
Q6. Find the distance between parallel lines
(i) 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0
(ii) l (x + y) + p = 0 and l (x + y) – r = 0
Q7. Find equation of the line parallel to the line 3x – 4y + 2 = 0 and passing through the point (–2, 3).
Q8. Give equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.
Q9. Calculate angles between the lines √3x+y=1 and x+√3y=1
Q10. A line passes through points (k, 3)(4, 1) intersects the line 7x – 9y – 19 = 0, at right angle. Find the value of k.
Q11. Prove that the line through the point (xa, ya) and parallel to the line Ax + By + C = 0 is A(x – xa) + B (y – ya) = 0.
Q12. The angle between the two lines is 60° at intersection and passes through the point (2, 3). Obtain the slope of a second line when the slope of first line is 2.
Q13 A line segment joining the points (4, 5) and (– 2, 3). Obtain the equation of the perpendicular bisector of the line segment.
Q14: Obtain the coordinates of the foot of perpendicular from the point (– 2, 4) to the line 3x – 4y – 16 = 0.
Q15: The normal meets point (– 2, 3), is drawn from the origin to the equation of line y = m x + c.Obtain the values of m and c.
Q16: Suppose r and s are the lengths from the lines x cos θ – y sin θ = n cos 2θ and x sec θ + y cosec θ = n to the origin perpendiculars, respectively, prove that r 2 + 4 s2 = n 2
Q17: The vertices of the triangle PQR are P (3, 4), Q (5, – 2) and R (2, 3), obtain how long the altitude is from the vertex P and also obtain the equation.
Q 18: Suppose ‘r’ is the length of the origin to the line from perpendicular from the normal. The line has axes i and j axes as intercepts of the line, then prove that:
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