Equation of chord joining points `P(alpha)` and `Q(beta)`

Equation of chord joining Chord P(alpha) and Q(beta)

If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^(2))/(a^(2)))+((y^(2))/(b^(2)))=1 subtends a right angle at the vertex A(a,0), then prove that tan((a)/(2))tan((beta)/(2))=-(b^(2))/(a^(2))

Auxilliary circle position OF point || Line & ellipse || Equation OF chord joining p(alpha), Q (beta), tangents, normaL || Highlights

Prove that the equation of the chord joining the points 'a'&'b' on the ellipse x^2/a^2+y^2/b^2=1 is x/a cos((alpha+beta)/2)+y/b sin((alpha+beta)/2)=cos((alpha-beta)/2)

Point of intersection of tangents at P(alpha) and Q(Beta)

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)

P and Q are two points on the rectangular hyperbola xy = C^(2) such that the abscissa of P and Q are the roots of the equations x^(2) - 6x - 16 = 0 . Equation of the chord joining P and Q is

If the circles described on the line joining the points (0,1) and (alpha,beta) as diameter cuts the X - axis in points whose abscissae are roots of equation x^(2)-5x+3=0 then (alpha,beta)=

Ellipse- Tangents and equation OF chord at A(alpha),B(beta) and question base on these topic

Q.Let p and q real number such that p!=0p^(2)!=q and p^(2)!=-q. if alpha and beta are non-zero complex number satisfying alpha+beta=-p and alpha^(3)+beta^(3)=q then a quadratic equation having (alpha)/(beta) and (beta)/(alpha) as its roots is