If `(alpha, beta)`, `(bar x, bar y) `and `(p, q)` are the coordinates of the circumcentre, the centroid and the orthocentre of a triangle, prove that :
`3barx=2alpha + p` and `3bary= 2beta+q`.

Find the centroid of the triangle whose orthocentre is (-3,5) and circumcentre is (6,2).

Let A(3,4) B(5,0), C(0,5) be the vertices of a triangle ABC then orthocentre of Delta ABC is (alpha, beta) Find alpha + beta

If alpha,beta are the roots of the equation x^2-2x+3=0 obtain the equation whose roots are alpha^3-3alpha^2+5alpha-2 and beta^3-beta^2+beta=5

If alpha,beta are the roots of the equation x^2-2x+3=0 obtain the equation whose roots are alpha^3-3alpha^2+5alpha-2 and beta^3-beta^2+beta+5

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta + alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is:

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is a. x^(2)+alpha x- beta=0 b. x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0 c. x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0 d. x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0

A circle with centre (3alpha, 3beta) and of variable radius cuts the rectangular hyperbola x^(2)-y^(2)=9a^(2) at the points P, Q, S, R . Prove that the locus of the centroid of triangle PQR is (x-2alpha)^(2)-(y-2beta)^(2)=a^(2) .

If alpha, beta be the roots of the equation x^2-px+q=0 then find the equation whose roots are q/(p-alpha) and q/(p-beta)

If A(alpha,1/alpha),B(beta,1/beta) "and" C(gamma,1/gamma) are the vertices of Delta ABC where alpha,beta are roots of x^(2)-6p_(1)x+2 =0 : beta,gamma are roots of x^(2)-6p_(2)x+3 = 0 and gamma, alpha are roots of x^(2)-6p_(3)x+6=0(p_(1),p_(2),p_(3) are positive) then find the co-ordinates of centroid of Delta ABC