The line joining `A(bcosalphabsinalpha)` and `B(acosbeta,asinbeta)` is produced to the point `M(x ,y)` so that `A M` and `B M` are in the ratio `b : adot` Then prove that `x+ytan(alpha+beta/2)=0.`

If alpha-beta= constant, then the locus of the point of intersection of tangents at P(acosalpha,bsinalpha) and Q(acosbeta,bsinbeta) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is: (a) a circle (b) a straight line (c) an ellipse (d) a parabola

The distance between the point ( acosalpha,asinalpha) and ( acosbeta,asinbeta) is (a) ( b ) (c) acos( d )(( e )alpha-beta)/( f )2( g ) (h) (i) (j) (b) ( k ) (l)2acos( m )(( n )alpha-beta)/( o )2( p ) (q) (r) (s) (c) ( d ) (e)2as in (f)(( g )alpha-beta)/( h )2( i ) (j)( k ) (l) (d) ( m ) (n) asin( o )(( p )alpha-beta)/( q )2( r ) (s) (t) (u)

If the chord joining points P(alpha)a n dQ(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(alpha/2)tan(beta/2)=-(b^2)/(a^2)dot

The line joining the points A(2,1),a n dB(3,2) is perpendicular to the line (a^2)x+(a+2)y+2=0. Find the values of adot

If x = cos alpha + i sin alpha , y = cos beta + i sin beta , prove that x^(m)y^(n)+1/(x^m y^n) = 2 cos (m alpha + n beta) .

If alpha and beta are the roots of the equation x^(2)-ax+b=0 ,find Q(b) (1)/(alpha)+(1)/(beta)

A ladder rest against a wall making an angle alpha with the horizontal. The foot of the ladder is pulled away from the wall through a distance x , so that it slides a distance y down the wall making an angle beta with the horizontal. Prove that x=ytan(alpha+beta)/2dot

If alpha, beta are the roots of the equation (x-a)(x-b)=5 then the roots of the equation (x- alpha)(x-beta)+5=0 are

If alpha and beta are the roots of the equation x^(2)-ax+b=0 ,find Q (a)(alpha)/(beta)+(beta)/(alpha)

If alphaa n dbeta(alpha