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+y=1, prove that sum_(r=0)^n .^nC_r x^r y^(n-r) = 1 .

If x^my^n = (x + y)^(m+n) , prove that (d^2y)/(dx^2)=0 .

If the points P(h , k),\ Q(x_1, y_1)a n d\ R(x_2, y_2) lie on a line. Show that: (h-x_1)(y_2-y_1)=(k-y_1)(x_2-x_1)dot

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

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

Find the condition, that the line lx + my + n = 0 may be a tangent to the circle (x - h)^(2) + (y - k)^(2) = r^(2) .

The length of projection of the segment join (x_1,y_1,z_1) and (x_2,y_2,z_20 on te line (x-alpha)/l=(y-beta)/m=(z-gamma)/n is (A) |l(x_2-x_1)+m(y_2-y_1)+n(z_2-z_1) (B) |alpha(x_2-x_1)+beta(y_2-y_1)+gamma(z_2-z_1)| (C) |(x_2-x_1)/l+(y_2-y_1)/m+(z_2-z_1)/n| (D) none of these

Find the middle point of the chord intercepted on line lx + my + n = 0 by circle x^2+y^2=a^2 .

If straight line lx + my + n=0 is a tangent of the ellipse x^2/a^2+y^2/b^2 = 1, then prove that a^2 l^2+ b^2 m^2 = n^2.