Determine the equation of straight line which is tangent at one point and normal at any point of the curve `x=3t^2 , y=2t^3`

Find the equation of the straight line which is a tangent at one point and normal at another point to the curve y=8t^(3)-1, x=4t^(2)+3 .

The equation of the straight lines which are both tangent and normal to the curve 27x^(2)=4y^(3) are

Find the equations of the tangent and the normal at the point ' t ' on the curve x=a\ s in^3t , y=b\ cos^3t .

Find the equation of the tangent and the normal at the point 't,on the curve x=a sin^(3)t,y=b cos^(3)t

Find the equation of the tangent and the normal at the point 't' on the curve x=a(t+sint), y=a(1-cost)

If a line is tangent to one point and normal at another point on the curve x=4t^(2)+3,y=8t^(3)-1, then slope of such a line is

Find the equation of normal to the curves x=t^(2),y=2t+1 at point

A curve y=f(x) passes through the point P(1,1) . The normal to the curve at P is a(y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point. Determine the equation of the curve. Also obtain the area bounded by the y-axis, the curve and the normal to the curve at P .

Equation of the tangent at the point t=-3 to the parabola y^(2)=3x is

Equation of the tangent at the point t=-3 to the parabola y^2 = 3x is