Slope of the tangent to a family of curve is given by byax. What is the slope of the tangent of the orthogonal trajectory of the curve?
The equation of the curves, satisfying the differential equation d2ydx2(x2+1)=2xdydx passing through the point (0,1) and having the slope of tangent at x=0 as 6 is
Draw a graph from the following data. Draw tangents at x = 2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve drawn is y=2x2 and the slope of tangent is tan θ=dydx=4x.