Misc 22 - Chapter 10 Class 11 Straight Lines (Important Question)
Last updated at Dec. 16, 2024 by Teachoo
Chapter 10 Class 11 Straight Lines
Ex 9.1, 7 Important
Ex 9.1, 8 Important
Question 2 Important
Question 1 Important
Ex 9.2, 13 Important
Ex 9.2, 17 Important
Question 7 Important
Ex 9.3, 4 Important
Ex 9.3, 7 Important
Ex 9.3, 9
Ex 9.3, 15 Important
Ex 9.3, 17 Important
Example 13 Important
Misc 5 Important
Misc 11 Important
Misc 17 Important
Misc 22 You are here
Chapter 10 Class 11 Straight Lines
Last updated at Dec. 16, 2024 by Teachoo
Misc 22 Prove that the product of the lengths of the perpendiculars drawn from the points (β(π^2 β π^2 ), 0) and ( β β(π^2 β π^2 ), 0) to the line π₯/π cos π + π¦/π sin π = 1 is b2 . Let point A be (β(π^2βπ^2 ), 0) & point B be (ββ(π^2βπ^2 ), 0) The given line is π₯/π cos ΞΈ + π¦/π sinΞΈ = 1 We need to show that Product of the length of perpendiculars from point A & point B to the line π₯/π cos ΞΈ + π¦/π sin ΞΈ = 1 is b2 Let p1 be the perpendicular distance from point A(β(π^2 β π^2 ), 0) to the line π₯/π cos ΞΈ + π¦/π sin ΞΈ = 1 & p2 be the perpendicular distance from point B( β β(π^2 β π^2 ), 0) to the line π₯/π cos ΞΈ + π¦/π sin ΞΈ = 1 We need to show p1 Γ p2 = b2 Calculating p1 & p2 Given line is (π₯ )/π cos ΞΈ + π¦/πsin ΞΈ = 1 (cosβ‘π/π) x + (sinβ‘π/π)y β 1 = 0 The above equation is of the form Ax + By + C = 0 Here A = cosβ‘π/π, B = sinβ‘π/π & C = β 1 We know that Distance of a point (x1, y1) from line Ax + By + C = 0 is d = |γπ΄π₯γ_1 + γπ΅π¦γ_1 + π|/β(π΄^2 + π΅^2 ) Perpendicular distance p1 of point A(β(π^2 β π^2 ), 0) from the line π₯/π cos ΞΈ + π¦/π sin ΞΈ = 1 is d = |γπ΄π₯γ_1 + γπ΅π¦γ_1 + π|/β(π΄^2 + π΅^2 ) Putting values p1 = |cosβ‘π/π β(π^2 + π^2 ) + sinβ‘π/π (0) + ( β 1)|/β((cosβ‘π/π)^2 + (sinβ‘π/π)^2 ) p1 = (β(π^2 β π^2 )/π cosβ‘π + 0 β 1)/β((γπππ γ^2 π)/π^2 + (γπ ππγ^2 π)/π^2 ) p1 = (β(π^2 β π^2 )/π cosβ‘π β 1)/β((γπππ γ^2 π)/π^2 + (γπ ππγ^2 π)/π^2 ) Perpendicular distance p2 of point B = ( β β(π^2 β π^2 ), 0) from the line π₯/π cos ΞΈ + π¦/π sin ΞΈ = 1 is d = |π΄π₯1 + π΅π¦1 + π|/β(π^2 + π^2 ) Putting values p2 = |cosβ‘π/π ( β β(π^2 β π^2 )) + sinβ‘π/π (0) + ( β 1)|/β((cosβ‘π/π)^2 + (sinβ‘π/π)^2 ) p2 = ( β β(π^2 β π^2 )/π cosβ‘π + 0 β 1)/β((cosβ‘π/π)^2 + (sinβ‘π/π)^2 ) p2 = ( β β(π^2 β π^2 )/π cosβ‘π β 1)/β(γπππ γ^2/π^2 + (γπ ππγ^2 π)/π^2 ) Finding p1p2