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Ex 9.3

Ex 9.3, 1 (i)

Ex 9.3, 1 (ii) Important

Ex 9.3, 1 (iii)

Ex 9.3, 2 (i)

Ex 9.3, 2 (ii)

Ex 9.3, 2 (iii) Important

Ex 9.3, 3

Ex 9.3, 4 Important

Ex 9.3, 5 (i) Important

Ex 9.3, 5 (ii)

Ex 9.3, 6

Ex 9.3, 7 Important

Ex 9.3, 8 Important

Ex 9.3, 9

Ex 9.3, 10

Ex 9.3, 11 Important You are here

Ex 9.3, 12

Ex 9.3, 13 Important

Ex 9.3, 14

Ex 9.3, 15 Important

Ex 9.3, 16 Important

Ex 9.3, 17 Important

Question 1 (i) Deleted for CBSE Board 2024 Exams

Question 1 (ii) Deleted for CBSE Board 2024 Exams

Question 1 (iii) Important Deleted for CBSE Board 2024 Exams

Last updated at May 29, 2023 by Teachoo

Ex 9.3, 11 Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line. We know that Angle between 2 lines be tan θ =|(𝑚_2 − 𝑚_1)/(1 + 𝑚_2 𝑚_1 )| Here m1 = Slope of one line = 2 θ = 60° (given) We need to find m2 Putting the values tan 60° = |(𝑚_2 − 2)/(1 + 2 × 𝑚_2 )| √3 = |(𝑚_2 − 2)/(1 + 2𝑚_2 )| |(𝑚_2 − 2)/(1 + 2𝑚_2 )|= √3 (𝑚_2 − 2)/(1 + 2𝑚_2 ) = ± √3 So, (𝑚_2 − 2)/(1 + 2𝑚_2 ) = √3 and (𝑚_2 − 2)/(1 + 2𝑚_2 ) = – √3 Taking (𝒎_𝟐 − 𝟐)/(𝟏 + 𝟐𝒎_𝟐 ) = √𝟑 m2 − 2 = √3(1 + 2m2) m2 − 2 = √3 + 2√3m2 m2 – 2√3m2 = √3 + 2 m2 (1 – 2√3) = 2 + √3 m2 = (2 + √3)/(1 − 2√3) Taking (𝒎_𝟐 − 𝟐)/(𝟏 + 𝟐𝒎_𝟐 ) = − √𝟑 m2 − 2 = − √3(1 + 2m2) m2 − 2 = − √3 − 2√3m2 m2 + 2√3m2 = −√3 + 2 m2 (1 + 2√3) = 2 − √3 m2 = (2 − √3)/(1 + 2√3) We know that equation of a line passing through (x1, y1) & having slope m is (y − y1) = m(x − x1) Equation of a line passing through (2, 3) & having slope (𝟐 + √𝟑)/(𝟏 − 𝟐√𝟑) is (y − 3) = ( (2 + √3))/(1 − 2√3) (x − 2) (1 − 2√3)(y − 3) = (2 + √3)(x − 2) 1(y − 3) − 2√3(y − 3) = 2(x – 2) + √3(x − 2) y – 3 − 2√3y + 6√3 = 2x – 4 + √3x − 2√3 y − 2√3y − 4x − √3x = – 6√3 – 2√3 – 4 + 3 y (1 − 2√3) − x(√3 + 2) = – 1 – 8√3 1 + 8√3 = x(√3 + 2) + y (2√3 – 1) (√𝟑 + 2)x + (2√𝟑 – 1)y = 1 + 8√𝟑 Equation of a line passing through (2, 3) & having slope (𝟐 − √𝟑)/(𝟏 + 𝟐√𝟑) is (y − 3) = (2 − √3)/(2√3 + 1)(x − 2) (2√3 + 1) (y − 3) = (2 − √3) (x − 2) 2√3 (y − 3) + 1 (y − 3) = 2(x − 2) − √3(x − 2) 2√3 (y − 3) + 1 (y − 3) = 2(x − 2) − √3(x − 2) 2√3y − 6√3 + y − 3 = 2x − 4 − √3x + 2√3 2√3y + y − 6√3 − 3 = 2x − √3x − 4 + 2√3 (2√3 + 1)y − 6√3 − 3 = (2 − √3)x − 4 + 2√3 (2√3 + 1)y = − (√3 − 2)x − 4 + 2√3 + 6√3 + 3 (2√3 + 1)y + (√3−2)x = 2√3 + 6√3 − 4 + 3 (√𝟑−𝟐)x + (2√𝟑 + 1)y = 8√𝟑 − 1 Hence the equation of lines is (√3 + 2)x + (2√3 – 1)y = 1 + 8√3 or (√3 − 2)x + (2√3 + 1)y = 8√3 − 1