Show that the product of the perpendiculars drawn from the two points `(+-sqrt(a^(2)-b^(2)),0)` upon the straight line `(x)/(a)costheta+(y)/(b)sintheta=1` is `b^(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 costheta + y/b sintheta=1 is b^2 .

Show that the product of the perpendiculars from the two points (+-4,0) upon the straight linee 3xcostheta+5ysintheta=15 is independent of theta .

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 coordinates of the foot of the perpendicular drawn from the point (2,-5) on the straight line x=y+1.

find the length of the perpendicular drawn from the point (2,1,-1) on the line x - 2y + 4z = 9

prove that the product of the perpendiculars drawn from the point (x_1, y_1) to the pair of straight lines ax^2+2hxy+by^2=0 is |(ax_1^2+2hx_1y_1+by_1^2)/sqrt((a-b)^2+4h^2)|

Find the foot of perpendicular drawn from the point (2, 2) to the line 3x - 4y + 5 = 0

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

Find the locus of the foot of the perpendicular drawn from the origin to the straight line which passes through the fixed point (a,b).

Find the locus of the foot of the perpendicular drawn from the center upon any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1.