If the normal to the rectangular hyperbola `xy = c^2` at the point `'t'` meets the curve again at `t_1` then `t^3t_1,` has the value equal to

If the normal at (ct,c/t) on the curve xy=c^2 meets the curve again in 't' , then :

The equation of the normal at the point 't' to the curve x=at^(2), y=2at is :

If the normals at points ' t_(1) " and ' t_(2) ' to the parabola y^(2)=4 a x meet on the parabola, then

The length of the subnormal at 't' on the curve x = a (t + sin t), y = a(1-cos t) is

The slope of the tangent to the curve x=t^(2)+3t-8,y=2t^(2)-2t-5 at the point (2,-1) is

The slope of the tangent to the curve x = t^(2) + 3t - 8, y = 2t^(2) - 2t - 5 at the point (2,-1) is

The slope of the tangent to the curve : x=a sin t, y = a(cos t+log "tan" (t)/(2)) at the point 't' is :

If the parametric equation of a curve is given by x = e^(t) cos t, y = e^(t) sin t , then the tangent to the curve at the point t = pi/4 makes with the x-axis of the angle.