The slopes of the tangents drawn from P to the parabola `y^2=4ax` are `m_1` and `m_2`, then show that : `m_1/m_2=k`, where k is a constant.

The line y=mx+1 is tangent to the parabola y^2=4x if m is _____.

If the tangents drawn from the point (-6,9) to the parabola y^2=kx are perpendicular to each other then find k.

IF the slope of the tangent to the circle S=x^2+y^2-13=0 at (2,3) is m, then the point (m,(-1)/m) is

Find the equation of the tangent and normal drawn to the curve y^4 - 4x^4 - 6xy = 0 at the point M(1,2)

If area bounded by the curve y^(2)=4ax and y=mx is a^(2)//3 , then the value of m, is

Show that m-1 is a factor of m^21-1 and m^22-1

Locate the centre of mass of the syste,m of three particles of masses m_1 = 1 kg, m_2 = 2 kg and m_3 = 3 kg which are placed at the corners of an equilateral triangle of side 1 m.

A line passes through points A(x_1,y_1) and B(h,k) .If the slope of the line is m then show that k-y_1=m(h-x_1)