If `(h, r)` is the foot of the perpendicular from `(x_1, y_1)` to `lx+my+n=0`, prove that : `(x_1-h)/l, = (y_1 - r)/m, = (lx_1 + my_1 +n)/(l^2 + m^2)`

If (alpha, beta) is the foot of perpendicular from (x_1, y_1) to line lx+my+n=0 , then (A) (x_1 - alpha)/l = (y_1 - beta)/m (B) (x-1 - alpha)/l) = (lx_1 + my_1 + n)/(l^2+m^2) (C) (y_1 - beta)/m = (lx_1 + my_1 +n)/(l^2 +m^2) (D) (x-alpha)/l = (lalpha+mbeta+n)/(l^2+m^2)

If x^(m)y^(n)=1, prove that (dy)/(dx)=-(my)/(nx)

The area (in square units ) of the quadrilateral formed by two pairs of lines l^(2) x^(2) - m^(2) y^(2) - n (lx + my) = 0 and l^(2) x^(2)- m^(2) y^(2) + n (lx - my ) = 0 , is

If lx + my + n = 0 is tangent to the parabola x^(2)=y , them

Show that if the axes are rectangular,the equation of the line through the point (x_(1),y_(1),z_(1)) at right angle to the lines (x)/(l_(1))=(y)/(m_(1))=(z)/(n_(1));(x)/(l_(2))=(y)/(m_(2))=(z)/(n_(2)) is (x-x_(1))/(m_(1)n_(2)-m_(2)n_(1))=(y-y_(1))/(n_(1)l_(2)-n_(2)l_(1))=(z-z_(1))/(l_(1)m_(2)-l_(2)m_(1))

A(x_1, y_1), B(x_2,y_2), C(x_3,y_3) are three vertices of a triangle ABC. lx+my+n=0 is an equation of the line L. If the centroid of the triangle ABC is at the origin and algebraic sum of the lengths of the perpendicular from O the vertices of triangle ABC on the line L is equal to, then sum of the squares of reciprocals of the intercepts made by L on the coordinate axes is equal to

The line lx+my+n=0 touches y^(2)=4ax

Find the equation of the plane through the line (x-x_1)/l_1=(y-y_1)/m_1=(z-z_1)/n_1 and parallel to the line (x-alpha)/l_2=(y-beta)/m_2=(z-gamma)/n_2