Find the product of the length of perpendiculars drawn from any point on the hyperbola `x^2-2y^2-2=0` to its asymptotes.

the locus of the foot of perpendicular drawn from the centre of the ellipse x^2+3y^2=6 on any point:

Find the length of the perpendicular from the point (1,-2,3) to the plane x - y + z = 5.

Find the area of the triangle formed by any tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 with its asymptotes.

Locus of the feet of the perpendiculars drawn from either foci on a variable tangent to the hyperbola 16y^2 -9 x^2 = 1 is

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^(2) - b^(2)) , 0) " and " (- sqrt(a^(2) - b^(2)), 0) to the line x/a cos theta + y/b sin theta = 1 " is " b^(2) .

Find the length of the perpendicular drawn from point (2,3,4) to line (4-x)/2=y/6=(1-z)/3dot

Find the length of the perpendicular drawn from point (2,3,4) to line (4-x)/2=y/6=(1-z)/3dot

Find the length and the foot of the perpendicular from the point (7,14 ,5) to the plane 2x+4y-z=2.

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^(2)-b^(2)), 0) and (-sqrt(a^(2)-b^(2)), 0) to the line (x)/(a)cos theta+(y)/(b)sin theta=1 is b^(2)

Find the equation of the two tangents from the point (1,2) to the hyperbola 2x^(2)-3y^2=6