If the three points `(p,q), (m,n)` and `(p-m,q-n)` are collinear then prove that `pn=qm`

If the points (p ,\ q),\ (m ,\ n) and (p-m ,\ q-n) are collinear, show that p n=q m .

Prove by using distance formula that the points P(1,2,3),Q(-1,-1,-1)a n dR(3,5,7) are collinear.

Three points A B and C are collinear . If points C , P and Q are collinear then will the point A,B,C,P and Q also be collinear ? Explain your answer with reasons:

Prove that the length of perpendiculars from points 'P(m^2,2m) Q (mn ,m+n) and R(n^2,2n)' to the line x cos^2theta+ysinthetacostheta+sin^2theta=0 are in G.P.

If in the expansion of (1 + x)^n , the coefficients of pth and qth terms are equal, prove that p+q=n+ 2 , where p!=q .

in a G.P (p+q)th term = m and (p-q) th term = n , then find its p th term

In a GP if the (m+n)th term is p and (m-n)th term is q then mth term is

If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next p terms, then prove that (m+n)(1/m-1/p)=(m+p)(1/m-1/n)dot

If tangent at P and Q to the parabola y^2 = 4ax intersect at R then prove that mid point of R and M lies on the parabola, where M is the mid point of P and Q.

If p+r=mq and (1)/(q)+(1)/(s)=(m)/(r ), then prove that : p:q=r:s .