`y^2=m(n^2-x^2)`,m,n are arbitray constants.

If tan frac (x)(2)= m/n , prove than m sin x+n cos x=n .

the equation of the chord of contact of the pair of tangents drawn to the ellipse 4x^2+9y^2=36 from the point (m ,n) where mdotn=m+n ,m ,n being nonzero positive integers, is

ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n points L_(1),L_(2),…,L_(n) on AB is divided in n+1 equal parts and L_(1)M_(1), L_(2)M_(2),…,L_(n)M_(n) are line segments paralllel to BC and M_(1), M_(2),….,M_(n) are on AC, then the sum of the lengths of L_(1)M_(1), L_(2)M_(2),...,L_(n)M_(n) is

If l_1, m_1, n_1 and l_2, m_2, n_2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m_1n_2 - m_2n_1, n_1l_2 - n_2l_1, l_1m_2-l_2-m_1

Let f(x)=lim_(m->oo){lim_(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then the range of f(x)

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

If x,yinR^+ and log_10(2x)+log_10y=2 , log_10x^2-log_10(2y)=4 and x+y=m/n ,Where m and n are relative prime , the value of m-3n^(6) is

If (l_(1), m_(1), n_(1)) , (l_(2), m_(2), n_(2)) are D.C's of two lines, then (l_(1)m_(2)-l_(2)m_(1))^2+(m_(1)n_(2)-n_(1)m_(2))^2+(n_(1)l_(2)-n_(2)l_(1))^2+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^2=