Short Answer TypeFind points on the curve 
 at which the tangents are (i) parallel to the x-axis (ii) parallel to the y-axis.
Long Answer TypeFind points on the curve 
 at which the tangents are (i) parallel to the x-axis (ii) parallel to the y-axis.
For the curve y = 4x3 – 2x5, find all the points at which the tangent passes through the origin.
Multiple Choice Questions
Long Answer TypeIf the curve αx2 + βy2 = 1 and α' x2 + β'y2 = 1 intersect orthogonally, prove that (α – α') β β') = (β – β') α α'.Â
The equations of two curves are
               
                    ...(1)
and          
                     ...(2)
Let curves (1) and (2) intersect at 
                          ...(3)
and      
                        ...(4)
Subtracting (4) from (3), we get,
              
At 
Similarly for second curve,
               
Since the two curves (1) and (2) intersect orthogonally,
    Â
Multiple Choice Questions
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