Tiêu đề Straight Line Engineering Question Bank Solution (HSC 27).pdf ✅

Rhombus Publications WRITTEN weMZ mv‡j BUET-G Avmv cÖkœvejx 1. GKwU mij‡iLvi x I y Aÿ Øviv LwÐZ AskØq abvZ¥K Ges g~jwe›`y †_‡K Aw1⁄4Z j¤^, mij‡iLv‡K mgwØLwÐZ K‡i| j‡¤^i •`N ̈© 7 GKK n‡j, mij‡iLvi mgxKiY wbY©q Ki| [BUET 23-24] mgvavb: awi, mij‡iLvi mgxKiY: xcos + ysin = p GLv‡b, p = 7 †h‡nZz, g~jwe›`y †_‡K Aw1⁄4Z j¤^, mij‡iLv‡K mgwØLwÐZ K‡i|   = 45 Y X 7 O  xcos45 + ysin45 = 7  x 2 + y 2 = 7  x + y – 7 2 = 0 (Ans.) 2. (k, – 3k), (5, k) Ges (– k, 2) we›`yÎq Øviv Drcbœ wÎfz‡Ri †ÿÎdj 28 eM©GKK, †hLv‡b k GKwU c~Y© msL ̈v| wÎfz‡Ri j¤^we›`yi ̄’vbv1⁄4 wbY©q Ki| [BUET 22-23] mgvavb: (k, – 3k), (5, k) Ges (– k, 2) cÖkœg‡Z, 1 2     k – 3k 5 k – k 2 k – 3k = 28  k 2 + 10 + 3k2 + 15k + k2 – 2k = 56  5k2 + 13k – 46 = 0  k = 2, – 23 5 wKš‘ (k  Z)  k = 2  ̄’vbv1⁄4 A(2, – 6); B(5, 2); C(– 2, 2) B C A O(x, y) awi, j¤^we›`y O(x, y)| AB I OC ci ̄úi j¤^ nIqvq, mAB  mOC = – 1  2 + 6 5 – 2  y – 2 x + 2 = – 1  3x + 8y = 10 .....(i) Avevi, AC I OB ci ̄úi j¤^ nIqvq, mAC  mOB = – 1  2 + 6 – 2 – 2  y – 2 x – 5 = – 1  x – 2y = 1 ....(ii) (i) I (ii) mgvavb K‡i, wb‡Y©q j¤^we›`y(x, y)      2  1 2 (Ans.) 3. (a – 1)x + y = a ........ (i) (2, 2)  (b, 0) ........... (ii) †iLvØq (K) j¤^ n‡j a I b Gi m¤úK© Kx? (L) mgvšÍivj n‡j a I b Gi m¤úK© Kx? [BUET 21-22] mgvavb: †`Iqv Av‡Q, (a – 1)x + y = a  y = – (a – 1)x + a GB †iLvi Xvj, m1 = – (a – 1) Ges (2, 2) Ges (b, 0) we›`y؇qi ms‡hvMKvix †iLvi Xvj m2 = 2 – 0 2 – b = 2 2 – b (K) †iLvØq j¤^ n‡j, m1m2 = – 1  – (a – 1) × 2 2 – b = – 1  2a – 2 = 2 – b  2a + b = 4 (Ans.) (L) †iLvØq mgvšÍivj n‡j, m1 = m2  – (a – 1) = 2 2 – b  (a – 1)(2 – b) = – 2  2a – ab – 2 + b = – 2  2a + b – ab = 0 (Ans.) 4. g~j we›`y n‡Z xsec – ycosec = k Ges xcos – ysin = kcos2 †iLv؇qi j¤^ `~iZ¡ h_vμ‡g 2 cm Ges 3 cm| k Gi gvb wbY©q Ki| [BUET 19-20] mgvavb: g~jwe›`y (0, 0) †_‡K xsec – ycosec – k = 0 †iLvi Dci j¤^`~iZ¡,       0 × sec – 0 × cosec – k sec2  + cosec2  = 2  k 2 1 cos2  + 1 sin2  = 4 [eM© K‡i]