`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 tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 make angles alphaa n dbeta with the major axis such that tanalpha+tanbeta=gamma, then the locus of their point of intersection is x^2+y^2=a^2 (b) x^2+y^2=b^2 x^2-a^2=2lambdax y (d) lambda(x^2-a^2)=2x y

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

Two tangents to the parabola y^2=4ax make supplementary angles with the x-axis. 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)

Two tangents to the parabola y^2 = 4ax make angles theta_1,theta_2 with the x-axis. Then the locus of their point of intersection if cot theta_1 + cot theta_2=c is

The equation of tangent to the ellipse 2x^(2)+3y^(2)=6 which make an angle 30^(@) with the major axis is

Find the equations of the tanggents to the ellipse (x ^(2))/(2) + (y ^(2))/(7) =1 that make an angle of 45 ^(@) with the x-axis.

Fnd the equation of the tangent to the ellipse (x ^(2))/(16) + (y ^(2))/(9) =1 which makes an angle of 30^(@) with the x-axis.

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

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 .