[" 5."16(x+y)^(2)-36(x-y)^(2)],[" 7."a^(2)-ac+bc-b^(2)]

(x^(2))/(36)+(y^(2))/(16)=1

Find the co-ordinates of the vertices, the foci, the eccentricity and the length of latus-rectum of the hyperbolas : (a) (x^(2))/(9) -(y^(2))/(16) = 1 (b) (i) 16x^(2) - 9y^(2) = 576 (ii) y^(2) -16x^(2) = 1 (iii) 5y^(2) - 9x^(2) = 36 (iv) 49y^(2) - 16x^(2) = 784 .

Factorize each of the following algebraic expressions: a^(2)+14a+48(2)x^(2)-4x-21y^(2)+5y-36(4)(a^(2)-5a)^(2)-36(a+7)(a-10)+16

Factorize :12x^(3)y^(3)+16x^(2)y^(5)-4x^(5)y^(2)18a^(3)b^(2)+36ab^(4)-24a^(2)b^(3)

{:("Column" A ,, "Column" B), ((3x^(2) - 5)- (2x^(2) - 5 + y^(2)) ,, (a) x^(2) + xy + y^(2)) , (9x^(2) - 16y^(2) ,, (b) 2) , ((x^(3) - y^(3))/(x-y) ,, (c) (9x + 16y) (9x - 16y)) , ("The degree of " (x + 2) (x+3) ,, (d) x^(2) - y^(2)) , (,, (e) 1) , (,, (f) (3x + 4y) (3x - 4y)):}

If the circles x^(2)+y^(2)-16x-20y+164=r^(2) and (x-4)^(2)+(y-7)^(2)=36 intersect at two points then (a) 1 11(d)0

If the circles x^(2)+y^(2) +5Kx+2y + K=0 and2(x^(2)+y^(2))+2Kx +3y-1=0, (KinR) , intersect at the points P and Q, then the line 4x + 5y - K = 0 passes through P and Q, for x^(2)+y^(2)-16x-20y+164=r^(2) and (x-4)^(2)+(y-7)^(2) = 36 intersect at two distinct points, then

Multiply : 3 - (2)/(3)xy + (5)/(7)xy^(2) - (16)/(21)x^(2)y by -21 x^(2)y^(2)

Comprehension (Q.5 & 6 ) Let AB be any chord of the circle x^(2)+y^(2)-2x-6y-6=0 which subtends a right angle at the point (2, 4).Locus of mid point of AB is x^(2)+y^(2)-7y-16=0x^(2)+y^(2)-3x-7y+7=0x^(2)+y^(2)+3x+7y-16=0x^(2)+y^(2)+3x+7y-7=0