Title Straight Line Varsity Question Bank Solution (HSC 27).pdf ✅

mij‡iLv  Varsity Question Bank Solution (HSC 27) 1 Rhombus Publications weMZ mv‡j DU-G Avmv cÖkœvejx 1. 3x + 7y = 21 Ges 2ax – 3by + 6 = 0 mgxKiYØq GKB mij‡iLv cÖKvk Ki‡j a Ges b Gi gvb KZ? [DU 24-25] a = 1, b = 2 a = – 3 7 , b = 2 3 a = 0, b = 1 a = 1 2 , b = 4 DËi: a = – 3 7 , b = 2 3 e ̈vL ̈v: GKB mij‡iLv cÖKvk Ki‡j, 3 2a = 7 – 3b = 21 – 6  a = 3  (– 6) 2  21 = – 3 7  b = 6  7 21  3 = 2 3 2. (1, 1) we›`yMvgx I 2x – 3y – 5 = 0 †iLvi Dci j¤^‡iLvi mgxKiY †KvbwU? [DU 23-24] 3x + 2y – 5 = 0 3x + 2y + 5 = 0 3x – 2y – 1 = 0 – 2x + 3y + 1 = 0 DËi: 3x + 2y – 5 = 0 e ̈vL ̈v: 3x + 2y = 3  1 + 2  1  3x + 2y – 5 = 0 3. (0, 2) Ges (– 2, 0) we›`yMvgx mij‡iLv x A‡ÿi abvZ¥K w`‡Ki mv‡_ Kx †KvY Drcbœ K‡i? [DU 22-23] 30 45 60 120 DËi: 45 e ̈vL ̈v: (0, 2) (– 2, 0) X Y X Y tan = 2 – 0 0 – (– 2) = 1   = 45 4. y A‡ÿi mgvšÍivj Ges 2x – 7y + 11 = 0 I x + 3y = 8 †iLv؇qi †Q`we›`y w`‡q AwZμgKvix mij‡iLvi mgxKiY †KvbwU? [DU 22-23, 17-18; JUST 19-20] 3x – 7 = 0 13x – 23 = 0 7x – 3 = 0 7x – 23 = 0 DËi: 13x – 23 = 0 e ̈vL ̈v: awi, wb‡Y©q mgxKiY: x = a 2x – 7y + 11 = 0  y = 2x + 11 7 ....... (i)  x + 3y = 8  x + 3  2x + 11 7 = 8 [(i) n‡Z]  7x + 6x + 33 = 56  13x – 23 = 0 5. y = 1 + 1 2 + x eμ‡iLv x Aÿ‡K A we›`y‡Z Ges y Aÿ‡K B we›`y‡Z †Q` Ki‡j AB mij‡iLvi mgxKiY wb‡Pi †KvbwU? [DU 22-23] x + 2y + 3 = 0 x + 2y – 3 = 0 x – 2y + 3 = 0 x – 2y – 3 = 0 DËi: x – 2y + 3 = 0 e ̈vL ̈v: x Aÿ ev y = 0 n‡j,  0 = 1 + 1 2 + x  2 + x = – 1  x = – 3  A(– 3, 0) y Aÿ ev x = 0 n‡j,  y = 1 + 1 2 + 0 = 1 + 1 2 = 3 2  B     0 3 2 AB †iLvi mgxKiY: x – 3 + y 3 2 = 1  – x + 2y = 3  x – 2y + 3 = 0 6. †Kv‡bv we›`yi †cvjvi ̄’vbv1⁄4 (c, ) n‡j, we›`ywUi Kv‡Z©mxq ̄’vbv1⁄4 KZ? [DU 21-22] (– 1, 0) (– c, 0) (c, – c) (– c, c) DËi: (– c, 0) e ̈vL ̈v: x = c.cos = – c y = c.sin = 0