Prove that the lengths of the perpendiculars from the points `(m^2,2m),(m m^(prime),m+m^(prime)),` and `(m^('2),2m^(prime))` to the line `x+y+1=0` are in GP.

The lengths of the perpendiculars from the points (m^(2), 2m), (mn, m+n) and (n^(2), 2n) to the line x+sqrt3y+3=0 are in

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^(2)theta+y sin theta cos theta+sin^(2)theta=0 are in G.P.

If p_(1),p_(2),p_(3) be the length of perpendiculars from the points (m^(2),2m),(mm',m+m') and (m^('2),2m') respectively on the line xcosalpha+ysinalpha+(sin^(2)alpha)/(cosalpha)=0 then p_(1),p_(2),p_(3) are in:

The lengths of the perpendiculars from (m^(2),2m),(mn,m+n) and (n^(2),2n) to the straight line os x cos alpha+y sin a+sin alpha tan alpha=0 are in

Show that the area of the triangle formed by the lines y=m_(1)x+c_(1),y=m_(2)x+c_(2) and and is 2|m_(1)-m_(2)|

The sum of all the prime factors of m is 9. Find the number m.

The perpendicular from the origin to the line y=m x+c meets it at the point (-1,2). Find the values of m\ a n d\ cdot

If theta is the acute angle between the lines with slopes m1 and m2 then tan theta=(m_(1)-m_(2))/(1+m_(1)m_(2)) 2) if p is the length the perpendicular from point P(x1,y1) to the line ax +by+c=0 then p=(ax_(1)+by_(1)+c)/(sqrt(a^(2)+b^(2)))