Tiêu đề Conics Practice Sheet HSC FRB 24.pdf ✅

KwYK  Final Revision Batch '24 1 06 KwYK Conics Board Questions Analysis m„Rbkxj cÖkœ †evW© mvj XvKv gqgbwmsn ivRkvnx Kzwgjøv h‡kvi PÆMÖvg ewikvj wm‡jU w`bvRcyi 2023 2 1 2 2 2 2 2 2 1 2022 2 2 2 2 1 2 2 2 2 eûwbe©vPwb cÖkœ †evW© mvj XvKv gqgbwmsn ivRkvnx Kzwgjøv h‡kvi PÆMÖvg ewikvj wm‡jU w`bvRcyi 2023 5 5 5 5 3 3 5 5 5 2022 5 5 5 5 5 5 5 6 5 weMZ mv‡j †ev‡W© Avmv m„Rbkxj cÖkœ 1| DÏxcK-1: 16x2 + 25y2 – 32x + 100y – 284 = 0 DÏxcK-2: Y Y X X C B P(6, 0) A(0, 4) O(0, 0) OC = 3 [XvKv †evW©- Õ23] (K) 4x2 – 9y2 = 36 Awae„‡Ëi AmxgZ‡Ui mgxKiY wbY©q Ki| (L) DÏxcK-1 Gi wbqvgK †iLvi mgxKiY wbY©q Ki| (M) DÏxcK-2 Gi wPÎwU GKwU cive„Ë Ges kxl©we›`y A n‡j, CB †iLvi •`N© ̈ wbY©q Ki| DËi: (K) y =  2 3 x ; (L) 3x – 28 = 0 ; 3x + 22 = 0 (M) 3 GKK 2| DÏxcK-1: GKwU Dce„‡Ëi Dc‡K›`a (– 2, 3) Ges Dr‡Kw›`aKZv 1 3 | DÏxcK-2: GKwU Awae„‡Ëi Dr‡Kw›`aKZv 3 , Dc‡K›`a؇qi ga ̈eZ©x `~iZ¡ 18| [XvKv †evW©- Õ23] (K) x 2 8 + y 2 4 = 1 Dce„‡Ëi e„nr A‡ÿi •`N© ̈ wbY©q Ki| (L) DÏxcK-1 Gi Dce„ËwUi wbqvg‡Ki mgxKiY x + 2y – 1 = 0 n‡j, Dce„‡Ëi mgxKiY wbY©q Ki| (M) Awae„‡Ëi AÿØq‡K ̄’vbv‡1⁄4i Aÿ a‡i DÏxcK-2 Gi Awae„‡Ëi mgxKiY wbY©q Ki| DËi: (K) 4 2 GKK (L) 14x2 + 11y2 – 4xy + 62x – 86y + 194 = 0 (M) 2x2 – y 2 = 54 3| `„k ̈Kí-1: 3x2 + 9x – 6y – 8 = 0 GKwU KwY‡Ki mgxKiY| `„k ̈Kí-2: GKwU KwY‡Ki †K›`a g~jwe›`y‡Z, Dc‡Kw›`aK j‡¤^i •`N© ̈ 10 I Dr‡Kw›`aKZv 1 3 | [ivRkvnx †evW©- Õ23] (K) 3y2 – 5x2 = 15 KwYKwUi Dc‡K›`a wbY©q Ki| (L) `„k ̈Kí-1 G DwjøwLZ KwYKwUi Dc‡Kw›`aK j‡¤^i cÖvšÍwe›`y؇qi ̄’vbv1⁄4 I wbqvgK‡iLvi mgxKiY wbY©q Ki| (M) ̄’vbv‡1⁄4i AÿØq‡K `„k ̈Kí-2 G ewY©Z KwY‡Ki AÿØq we‡ePbv K‡i Gi mgxKiY wbY©q Ki| DËi: (K) (0   2 2) (L)    –  5 2  – 47 24 I    –  1 2  – 47 24 ; 24y + 71 = 0 (M) 4x2 + 6y2 = 225 4| `„k ̈Kí-1: GKwU cive„‡Ëi kxl©we›`y (1, 1) Ges wbqvgK‡iLvi mgxKiY, 2x + y – 1 = 0 `„k ̈Kí-2: X S(–12, 6) A C A S(12, 6) X Y Y [ivRkvnx †evW©- Õ23] (K) 2x2 + y2 = 2 KwYKwUi kxl©we›`yi ̄’vbv1⁄4 wbY©q Ki|
2  Higher Math 2nd Paper Chapter-6 (L) `„k ̈Kí-1 Gi Av‡jv‡K cive„‡Ëi mgxKiY wbY©q Ki| (M) `„k ̈Kí-2 Gi Dr‡Kw›`aKZv 3 n‡j KwYKwUi AmxgZU †iLvi mgxKiY wbY©q Ki| DËi: (K) kxl©we›`yi ̄’vbv1⁄4 (0,  b)  (0   2) (L) (x – 2y)2 – 14x – 12y + 25 = 0 ; (M) y = 6  2 2x 5| f(x, y) = x2 – 4y2 – 6x – 16y – 11 Ges g(x, y) = 4y2 – 20x – 4y + 30 [h‡kvi †evW©- Õ23] (K) x 2 – 4y – 2 = 0 cive„ËwUi Aÿ‡iLvi mgxKiY wbY©q Ki| (L) f(x, y) = 0 KwY‡Ki cÖK...wZ wbY©q K‡i Dnvi Dc‡K›`a؇qi ga ̈eZ©x `~iZ¡ wbY©q Ki| (M) g(x, y) = 4y – 9 n‡j, KwYKwUi Aÿ‡iLv I wbqvg‡Ki †Q`we›`y wbY©q Ki| DËi: (K) Aÿ‡iLvi mgxKiY x = 0 ; (L) Awae„Ë ; 2 5 ; (M) Aÿ‡iLv I wbqvgK †iLvi †Q`we›`y     1 2  1 6| X Y Y B X O A S(0, 3) A(3, 2) B [h‡kvi †evW©- Õ23] (K) 9x2 – 4y2 = 36 KwY‡Ki wbqvg‡Ki mgxKiY wbY©q Ki| (L) A †K kxl©we›`y I S †K Dc‡K›`a a‡i Aw1⁄4Z cive„‡Ëi mgxKiY wbY©q Ki| (M) DÏxc‡K OB = 4 Ges AS = AS n‡j, BB †K e„nr Aÿ I AA †K ÿz`a Aÿ a‡i Aw1⁄4Z Dce„‡Ëi Dc‡Kw›`aK j‡¤^i mgxKiY †ei Ki| DËi: (K) 13x =  4 ; (L) (y – 3)2 = – 8 (x – 2) (M) y – 3  3 5 = 0 7| Y O X S M Z(1, 1) A(2, 2) Aÿ wØKvÿ     `„kKí-1 `„k ̈Kí-2: 4x2 + 5y2 + 10y – 16x + 1 = 0 [Kzwgjøv †evW©- Õ23] (K) y 2 = 4(4 – x) cive„‡Ëi kxl©we›`yi ̄’vbv1⁄4 wbY©q Ki| (L) `„k ̈Kí-1 n‡Z cive„ËwUi Dc‡K›`a I wbqvg‡Ki mgxKiY wbY©q Ki| (M) `„k ̈Kí-2 n‡Z KwYKwUi Dc‡K›`a I Dc‡Kw›`aK j‡¤^i •`N© ̈ wbY©q Ki| DËi: (K) kxl©we„›`yi ̄’vbv1⁄4 (4, 0) (L) wb‡Y©q cive„ËwUi Dc‡K›`a (3, 3) Ges wbqvgK‡iLvi mgxKiY, x + y – 2 = 0 (M) Dc‡K›`aØq (3, – 1) Ges (1, – 1) ; Dc‡Kw›`aK j‡¤^i •`N© ̈ 8 5 8| `„k ̈Kí-1: Y X   S P X y 2 = 16x Y O `„k ̈Kí-2: x 2 – 3y2 – 4x – 8 = 0 [Kzwgjøv †evW©- Õ23] (K) 4x2 + 5y2 = 1 Dce„ËwUi Dr‡Kw›`aKZv wbY©q Ki| (L) `„k ̈Kí-1 G S Dc‡K›`a Ges SP = 6 GKK n‡j, P we›`yi ̄’vbv1⁄4 wbY©q Ki| (M) `„k ̈Kí-2 Gi KwYKwUi Dc‡Kw›`aK j‡¤^i mgxKiY I •`N© ̈ wbY©q Ki| DËi: (K) 1 5 ; (L) P we›`yi ̄’vbv1⁄4 (2  4 2) (M) Dc‡Kw›`aK j‡¤^i •`N© ̈ 4 3 ; wb‡Y©q Dc‡Kw›`aK j‡¤^i mgxKiY, x – 6 = 0, x + 2 = 0 9| `„k ̈Kí-1: x = by2 + cy + a GKwU KwYK| `„k ̈Kí-2: †Kv‡bv cive„‡Ëi Dc‡Kw›`aK j‡¤^i cÖvšÍ-we›`yØq (– 2, 2) Ges (– 4, 2)| [PÆMÖvg †evW©- Õ23] (K) x 2 – 4y2 = 2 KwY‡Ki Dr‡Kw›`aKZv wbY©q Ki| (L) `„k ̈Kí-2 †_‡K cive„‡Ëi mgxKiY wbY©q Ki| (M) `„k ̈Kí-1 G KwY‡Ki kxl©we›`y (1, – 2) Ges GwU (3, 0) we›`yMvgx n‡j a, b, c Gi gvb wbY©q Ki| DËi: (K) 5 2 ; (L) – 2     y – 5 2 ; 2     y – 3 2 (M) a = 3, b = 1 2 , c = 2 10| `„k ̈Kí-1: C A Z M D(1, 1) S(1,–1) x – y – 4 = 0    Dce„‡Ëi Dc‡K›`a S Ges wbqvgK MZ `„k ̈Kí-2: 5x2 + 4y2 – 10x – 8y – 11 = 0 [PÆMÖvg †evW©- Õ23]
KwYK  Final Revision Batch '24 3 (K) y 2 = – 6x cive„‡Ëi Dc‡Kw›`aK j‡¤^i •`N© ̈ wbY©q Ki| (L) `„k ̈Kí-1 †_‡K Dce„‡Ëi mgxKiY wbY©q Ki| (M) `„k ̈Kí-2 †_‡K KwYKwUi wbqvg‡Ki mgxKiY wbY©q Ki| DËi: (K) 6 ; (L) 0 ; (M) – 4 11| M  Z A S [wm‡jU †evW©- Õ23] wP‡Îi cive„ËwUi Dc‡K›`a S, kxl© A Ges MZ wbqvgK‡iLv| (K) 3x2 – 4y + 6x – 5 = 0 cive„‡Ëi wbqvgK‡iLvi mgxKiY wbY©q Ki| (L) DÏxc‡K DwjøwLZ A I S we›`yi ̄’vbv1⁄4 h_vμ‡g (2, 3) I (2, 7) n‡j, cive„ËwUi mgxKiY wbY©q Ki| (M) A we›`yi ̄’vbv1⁄4 (– 1, 3) Ges MZ †iLvi mgxKiY 2x – 3y + 2 = 0 n‡j, cive„‡Ëi Dc‡Kw›`aK j‡¤^i mgxKiY wbY©q Ki| DËi: (K) 0 ; (L) 3x2 + 3y2 + 2xy – 8 = 0 ; (M) y = 6, y = – 4 12| `„k ̈Kí: X X A S C S A B B Y Y L     3 2  4 L     3 2  – 4  `„k ̈Kí-2: 4x2 – 9y2 – 16x + 54y – 101 = 0 [wm‡jU †evW©- Õ23] (K) 3x2 + 2y2 = 1 Dce„ËwUi Dr‡Kw›`aKZv wbY©q Ki| (L) `„k ̈Kí-1 Gi Dce„ËwUi Dr‡Kw›`aKZv 1 3 n‡j, Gi mgxKiY wbY©q Ki| (M) `„k ̈Kí-2 Gi KwYKwUi Dc‡K‡›`ai ̄’vbv1⁄4 wbY©q Ki| DËi: (K) 1 3 ; (L) 4x2 81 + y 2 18 = 1 (M) Dc‡K›`aØq (2 + 13  3) I (2 – 13  3) 13| `„k ̈Kí-1: f(y) = ay2 + by + c `„k ̈Kí-2: Z  S(4, 2) A(1, 2)   A kxl©we›`y I S Dc‡K›`a [ewikvj †evW©- Õ23] (K) y 2 = 8x + 5 KwY‡Ki wbqvg‡Ki mgxKiY wbY©q Ki| (L) `„k ̈Kí-1 Gi Av‡jv‡K, x = f(y) KwY‡Ki kxl©we›`y (3, – 2) Ges GwU (5, 0) we›`yMvgx n‡j a, b, c Gi gvb wbY©q Ki| (M) `„k ̈Kí-2 n‡Z cive„‡Ëi mgxKiY wbY©q Ki| DËi: (K) 8x + 21 = 0 ; (L) a = 1 2 , b = 2, c = 5 (M) y 2 – 12x – 4y + 16 = 0 14|  A(4, 0) S(5, 0)  X A(– 4, 0)   S(– 5, 0) X Y Y O [ewikvj †evW©- Õ23] (K) 9x2 – 4y2 = 36 KwY‡Ki AmxgZ‡Ui mgxKiY wbY©q Ki| (L) DÏxc‡Ki mvnv‡h ̈ Awae„‡Ëi mgxKiY wbY©q Ki| (M) DÏxc‡Ki A I A †K Dc‡K›`a a‡i Dce„‡Ëi mgxKiY wbY©q Ki hvi GKwU wbqvg‡Ki mgxKiY, 5x – 36 = 0 DËi: (K) y =  b a x  y =  3 2 x ; (L) 9x2 – 16y2 = 144 (M) 5x2 144 + 5y2 64 = 1 15| `„k ̈Kí-1: P(x, y) Y M S( Z –1,1) X X M Y x + 2y – 3= 0 O `„k ̈Kí-2:  S(4, 0) X Y O  S(– 4, 0) X Y [w`bvRcyi †evW©- Õ23] (K) x 2 = 8(1 – y) cive„‡Ëi wbqvgK †iLvi mgxKiY wbY©q Ki| (L) `„k ̈Kí-1 n‡Z P Gi mÂvic_wUi mgxKiY wbY©q Ki †hLv‡b Dr‡Kw›`aKZv 1 3 , Dc‡K›`a S Ges wbqvgK †iLv MZM
4  Higher Math 2nd Paper Chapter-6 (M) `„k ̈Kí-2 G S I S Dc‡K›`a, †K›`a n‡Z wbqvgK †iLvi `~iZ¡ 3 GKK n‡j, Awae„ËwUi mgxKiY Ges AmxgZ‡Ui mgxKiY wbY©q Ki| DËi: (K) y = 3 ; (L) 44x2 + 41y2 – 4xy + 96x – 78y + 81 = 0 ; (M) x 2 – 3y2 = 12 ;  1 3 x 16| `„k ̈Kí-1: 4x2 – 9y2 – 16x + 54y – 101 = 0. `„k ̈Kí-2: Z  A(1, 3)  M y = 4 M [gqgbwmsn †evW©- Õ23] (K) x 2 5 – y 2 3 = 1 Awae„ËwUi AmxgZ‡Ui mgxKiY wbY©q Ki| (L) `„k ̈Kí-1 Gi KwYKwU‡K cÖgvY AvKv‡i cÖKvk K‡i Dc‡Kw›`aK j‡¤^i •`N© ̈ I wbqvgK‡iLvi mgxKiY wbY©q Ki| (M) `„k ̈Kí-2 Gi cive„ËwUi mgxKiY wbY©q Ki| DËi: (K)  3 5 x ; (L) 8 3 ; 2  9 13 ; (M) x 2 – 2x + 4y – 11 = 0 17| DÏxcK-1: 3x2 – 4y – 6x – 5 = 0 DÏxcK-2: A(3, 2) P(x, y) M Z M S(0, 2) [XvKv †evW©- Õ22] (K) KwYK I KwY‡Ki Dc‡K‡›`ai msÁv wjL| (L) DÏxcK-1 G DwjøwLZ mgxKiYwU‡K cive„‡Ëi Av`k© mgxKiY AvKv‡i cÖKvk Ki I kxl©we›`y, Dc‡K›`a, A‡ÿi mgxKiY wbY©q Ki| (M) DÏxcK-2 G wPwýZ cive„‡Ëi mgxKiY wbY©q Ki| DËi: (L) (x – 1)2 = 4. 1 3 (y + 2) hv Av`k© AvKv‡ii cive„‡Ëi mgxKiY kxl©we›`y(1, – 2) ; Dc‡K›`a     1 – 5 3 ; x = 1 (Ans.) (M) y 2 – 4y + 12x – 32 = 0 18| DÏxcK-1: A(– 3, 0) X A(3, 0) B(0, 1) B(0, –1) Y Y X DÏxcK-2: M Z M P(x, y) S(1, 1) 2x + y = 1 n‡jv w`Kvÿ MM Gi mgxKiY| [XvKv †evW©- Õ22] (K) 2x2 + 3y2 = 1 Dce„ËwUi Dc‡Kw›`aK j‡¤^i •`N© ̈ wbY©q Ki| (L) DÏxcK-1 G DwjøwLZ Dce„‡Ëi Dr‡Kw›`aKZv, Dc‡K›`a wbqvg‡Ki mgxKiY wbY©q Ki| (M) DÏxcK-2 G DwjøwLZ Awae„‡Ëi Dr‡Kw›`aKZv 3 n‡j Gi mgxKiY wbY©q Ki| DËi: (K) 2 2 3 GKK ; (L) 2 2 3 ; ( 2 2  0) ;  9 2 2 (M) 7x2 – 2y2 + 12xy – 2x + 4y – 7 = 0 19| DÏxcK-1: M S M Z X X Y Y O A OA = OS = 1 DÏxcK-2: X Y Y X S A O A B AA = 6, AO < OB [ivRkvnx †evW©- Õ22]