Divide: `m^3-14 m^2+37 m-26\ b y\ m^2-12 m+13` `x^4+x^2+1\ b y\ x^2+x+1`

Divide: 9m^(5)+12m^(4)-6m^(2) by 3m^(2)24x^(3)y+20x^(2)y^(2)-4xy by 2xy

y-1=m_1(x-3) and y - 3 = m_2(x - 1) are two family of straight lines, at right angled to each other. The locus of their point of intersection is: (A) x^2 + y^2 - 2x - 6y + 10 = 0 (B) x^2 + y^2 - 4x - 4y +6 = 0 (C) x^2 + y^2 - 2x - 6y + 6 = 0 (D) x^2 + y^2 - 4x - by - 6 = 0

Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively. Column I, Column 2, Column 3 I, x^2+y^2=a , (i), m y=m^2x+a , (P), (a/(m^2),(2a)/m) II, x^2+a^2y^2=a , (ii), y=m x+asqrt(m^2+1) , (Q), ((-m a)/(sqrt(m^2+1)), a/(sqrt(m^2+1))) III, y^2=4a x , (iii), y=m x+sqrt(a^2m^2-1) , (R), ((-a^2m)/(sqrt(a^2m^2+1)),1/(sqrt(a^2m^2+1))) IV, x^2-a^2y^2=a^2 , (iv), y=m x+sqrt(a^2m^2+1) , (S), ((-a^2m)/(sqrt(a^2m^2+1)),(-1)/(sqrt(a^2m^2+1))) The tangent to a suitable conic (Column 1) at (sqrt(3),1/2) is found to be sqrt(3)x+2y=4, then which of the following options is the only CORRECT combination? (IV) (iii) (S) (b) (II) (iii) (R) (II) (iv) (R) (d) (IV) (iv) (S)

If y = 2x + m is a diameter to the circle x^(2) + y^(2) + 3x + 4y - 1 = 0 , then find m

Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively. Column I, Column 2, Column 3 I, x^2+y^2=a , (i), m y=m^2x+a , (P), (a/(m^2),(2a)/m) II, x^2+a^2y^2=a , (ii), y=m x+asqrt(m^2+1) , (Q), ((-m a)/(sqrt(m^2+1)), a/(sqrt(m^2+1))) III, y^2=4a x , (iii), y=m x+sqrt(a^2m^2-1) , (R), ((-a^2m)/(sqrt(a^2m^2+1)),1/(sqrt(a^2m^2+1))) IV, x^2-a^2y^2=a^2 , (iv), y=m x+sqrt(a^2m^2+1) , (S), ((-a^2m)/(sqrt(a^2m^2+1)),(-1)/(sqrt(a^2m^2+1))) If a tangent to a suitable conic (Column 1) is found to be y=x+8 and its point of contact is (8,16), then which of the followingoptions is the only CORRECT combination? (III) (ii) (Q) (b) (II) (iv) (R) (I) (ii) (Q) (d) (III) (i) (P)

Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively. Column I, Column 2, Column 3 I, x^2+y^2=a , (i), m y=m^2x+a , (P), (a/(m^2),(2a)/m) II, x^2+a^2y^2=a , (ii), y=m x+asqrt(m^2+1) , (Q), ((-m a)/(sqrt(m^2+1)), a/(sqrt(m^2+1))) III, y^2=4a x , (iii), y=m x+sqrt(a^2m^2-1) , (R), ((-a^2m)/(sqrt(a^2m^2+1)),1/(sqrt(a^2m^2+1))) IV, x^2-a^2y^2=a^2 , (iv), y=m x+sqrt(a^2m^2+1) , (S), ((-a^2m)/(sqrt(a^2m^2+1)),(-1)/(sqrt(a^2m^2+1))) For a=sqrt(2),if a tangent is drawn to a suitable conic (Column 1) at the point of contact (-1,1), then which of the following options is the only CORRECT combination for obtaining its equation? (I) (ii) (Q) (b) (III) (i) (P) (II) (ii) (Q) (d) ("I")("i")("P")

If x+2 is a factor of x^2+m x+14 , then m= 7 (b) 2 (c) 9 (d) 14

If the tangent to the curve x^(3)-y^(2) = 0 at (m^(2), -m^(2)) is parallel to y= -(1)/(m) x-2m^(3) , then the value of m^(3) is