(a^(2)-3b^(2))x^(2)+8abxy+(b^(2)-3a^(2))y^(2)=0

Find the angle between the pair of straight lines given by (a^(2)-3b^(2))x^(2)+8ab xy+(b^(2)-3a^(2))y^(2)=0

If a/b = x/y , then show that (a+b) (a^(2)+b^(2))x^(3) = (x+y)(x^(2)+y^(2))a^(3)

Factorise : (a-b)^(2)x^(2)+4abxy -(a+b)^(2)y^(2)

Locus of centroid of the triangle whose vertices are (a cos t,a sin t),(b sin t-b cos t)and(1,0) where t is a parameter is: (3x-1)^(2)+(3y)^(2)=a^(2)-b^(2)(3x-1)^(2)+(3y)^(2)=a^(2)+b^(2)(3x+1)^(2)+(3y)^(2)=a^(2)+b^(2)(3x+1)^(2)+(3y)^(2)=a^(2)-b^(2)

Show that straight lines (A^2-3b^2)x^2+8A Bx y(b^2-3A^2)y^2=0 form with the line A x+B y+C=0 an equilateral triangle of area (C^2)/(sqrt(3(A^2+B^2))) .

Add: (i) 3a - 2b + 5c, 2a + 5b - 7c, -a - b + c (ii) 8a - 6ab + 5b, -6a - ab - 8b, -4a + 2ab + 3b (iii) 2x^(3) - 3x^(2) + 7x - 8, -5x^(3) + 2x^(2) - 4x + 1, 3 - 6x + 5x^(2) - x^(3) (iv) 2x^(2) - 8xy + 7y^(2) - 8xy^(2), 2xy^(2) + 6xy - y^(2) + 3x^(2), 4y^(2) - xy - x^(2) + xy^(2) (v) x^(3) + y^(3) - z^(3) + 3xyz, - x^(3) + y^(3) + z^(3) - 6xyz, - x^(3) - y^(3) - z^(3) - 8xyz (vi) 2 + x - x^(2) + 6x^(3). -6 - 2x + 4x^(2) - 3x^(3). 2 + x^(2). 3 - x^(3) + 4x - 2x^(2)

Show that straight lines (A^2-3B^2)x^2+8A Bx y+(B^2-3A^2)y^2=0 form with the line A x+B y+C=0 an equilateral triangle of area (C^2)/(sqrt(3)(A^2+B^2)) .

Show that straight lines (A^2-3B^2)x^2+8A Bx y+(B^2-3A^2)y^2=0 form with the line A x+B y+C=0 an equilateral triangle of area (C^2)/(sqrt(3)(A^2+B^2) .

Show that straight lines (A^2-3B^2)x^2+8A Bx y(B^2-3A^2)y^2=0 form with the line A x+B y+C=0 an equilateral triangle of area (C^2)/(sqrt(3(A^2+B^2))) .