If the pair of lines `2x^(2)+3xy+y^(2)=0` makes angles `theta_(1),theta_(2)` with `x`-axis then `tan(theta_(1)-theta_(2))=`

Tangents to the ellipse b^(2)x^(2)+a^(2)y^(2)=a^(2)b^(2) makes angles theta_(1) and theta_(2) with major axis such that cot theta_(1)+cot(theta_(2))=k Then the locus of the point of intersection is

The tangent to y^(2)=ax make angles theta_(1)andtheta_(2) with the x-axis. If costheta_(1)costheta_(2)=lamda , then the locus of their point of intersection is

If a line makes angles theta_(1), theta_(2), theta_(3) with the coordinates planes, then sin^(2)theta_(1)+sin^(2)theta_(2)+sin^(2)theta_(3)= ………….

If the acute angle between the pairs of lines 3x^(2)-7xy+4y^(2)=0 and 6x^(2)-5xy+y^(2)=0 be theta_(1) and theta_(2) respectively, then (A) theta_(1)=theta_(2) (B) theta_(1)=2 theta_(2) (C) 2 theta_(1)=theta_(2) (C) 2 theta_(1)=theta_(2) (D) None of these

The tangents to x^(2)+y^(2)=r^(2) having inclinations theta_(1),theta_(2) intersect at P .If tan theta_(1)-tan theta_(2)=1 locus of P is

If tan theta_(1),tan theta_(2),tan theta_(3) are the real roots of the x^(3)-(a+1)x^(2)+(b-a)x-b=0, where theta _(1)+theta_(2)+theta_(3)in(0,pi), then theta_(1)+theta_(2)+theta_(3) ,is equal to pi/2 b.pi/4c.3 pi/4d. pi

Tangents drawn from point P to the circle x^(2)+y^(2)=16 make the angles theta_(1) and theta_(2) with positive x-axis. Find the locus of point P such that (tan theta_(1)-tan theta_(2))=c ( constant) .

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

Tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angle theta_(1),theta_(2) with transverse axis of a hyperbola.Show that the point of intersection of these tangents lieson the curve 2xy=k(x^(2)-a^(2)) when tan theta_(1)+tan theta_(2)=k

A projectile is projected in xy-plane with a speed of 10 m/s at an angle theta to the horizontal x-axis such that it passes through point (2,3). If two angles possible are theta_(1) and theta_(2) , find tan theta_(1)-theta_(2) .