If the tangents to ellipse `x^2/a^2 + y^2/b^2 = 1` makes angle `alpha and beta` with major axis such that `tan alpha + tan beta = lambda` then locus of their point of intersection is

If the tangents to the ellipse a 2 x 2 ​ + b 2 y 2 ​ =1 make angles α and β with the major axis such that tanα+tanβ=λ, then the locus of their point of intersection is

If the tangent at any point of the ellipse (x^2)/(a^3)+(y^2)/(b^2)=1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosbeta/(cosalpha)

If the lines px^2-qxy-y^2=0 makes the angles alpha and beta with X-axis , then the value of tan(alpha+beta) is

Tangents are drawn to the ellipse x^2/a^2+y^2/b^2=1 at two points whose eccentric angles are alpha-beta and alpha+beta The coordinates of their point of intersection are

Tangents drawn from the point (c, d) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angles alpha and beta with the x-axis. If tan alpha tan beta=1 , then find the value of c^(2)-d^(2) .

(1+tan alpha tan beta)^2 + (tan alpha - tan beta)^2 =

The tangents from (alpha, beta) to the ellipse x^2/a^2 + y^2/b^2 = 1 intersect at right angle. Show that the locus of the point of intersection of normals at the point of contact of the two tangents is the line ay-betax=0 .

lf cos^2 alpha -sin^2 alpha = tan^2 beta , then show that tan^2 alpha = cos^2 beta-sin^2 beta .

If the eccentric angles of the extremities of a focal chord of an ellipse x^2/a^2 + y^2/b^2 = 1 are alpha and beta , then (A) e = (cos alpha + cos beta)/(cos (alpha + beta)) (B) e= (sin alpha + sin beta)/(sin(alpha + beta)) (C) cos((alpha-beta)/(2)) = e cos ((alpha + beta)/(2)) (D) tan alpha/2.tan beta/2 = (e-1)/(e+1)

If alpha+beta=pi/4 then (1+tan alpha)(1+tan beta)=