Question

a. If the axes are translated to the point (-1, 3), then find the new equation of r? + y2 - 2x + 3y + 1 = 0. b. Answer the following. Check whether three points A(-1,-5). 813,-2) and C -8.1) lie on a line or not. ii. Find equation of the line joining the points (0.1) and (-1,-5). Prove that the point (1 ) does not lie on it. Question 2: a. Consider the homogeneous equation of pair of lines 2x? - Sxy + 2y = 0. i. Find the equation of lines. . Find the angle between the above lines ill. Find the equation of the bisectors of the angle between the lines. b. Show thot: line 2x + y = 11 intersects the circle x? + y = 26. Question 3 Find the type of a curve if y? - 2y - 2x + 4 = 0. Sketch the graph of 4x + 2y = 16. ill. Find the centre, the foci, vertices and directrices of the hyperbola 4x2 - y = 4.

هندسه تحليليه ابي حل كامل
الحين

Answer 1

x² + y ² - 2 2 +39 + 1 = 0 anis are translated to the point (-1,3) so new coordinate boot x = 92 y + 3 x= x+1, y = 9-3 (x+1) ² + (y'-3) 2-2 (2 + 1) +3 (9-3)+120 +231'+1 + y<cy'tg - 24'4+2 +3y!_9 +150 arty, 2-3 41 = 0 AC +1-5) B (3,-2) c # 8, X A B = V1G+ 40 Be= 12149, AC= Jugtis ABC A (-1,-5), B(3, 2), C (-8, 1) AB=√16+9 =5 , BC= V12Hg = 5130 - Ace 49+36 = 585 so three point not lie on a line (1,5) Acord Que 2 y-1 = -f(x-0) y-1 = 60 = y =6xt I C (1,7) does not satisfies the egn, 2x²-5ay +2y = 0 20² - Any-ry +2y²=0 us 2x [ax-2y] -y [x-2y] =0 (2x-4) (x-2y)=0 Teacherature

y=2x Pago No Pago No.- Date - y = 1/2 x angle btw 2 - 1/2 tano = 1 + 2x 1 o=tan 314 equation of er y = x Angle bisector and y=-x and o tand = - line zuty all interseets x²+42_26 y=11-22 x + (11-22 ) ² = 26 x² + 4x²_44x+121=26 5x²_uunt .95 D=442-5x95x 4 = 3670 so line intersects n+g2=26 y²-24 - 2x +4=0 +1-22+3=0 (4-1) - 2 (x-3) =0 14-1² 212-3, this is egn of para bolla. Que - (4-1)=212-3). Teacher Signature

Page No. Date (ii) 4x² + 2y² = 16 252) a=2, b=282 ellipse. 4 x² - y2 = 4 2 en vertices are a=1, 6²4 - Foci are cout 5) - direction along a arus - length of the transeuse ani २१-2