Curve Sketching
Symmetry
1 . If powers of y in a equation of curve are all even , then curve is symmetrical about X-axis .
2 . If powers of x in a equation of curve are all even , then curve is symmetrical about Y-axis .
3 . When x is replaced by -x and y is replaced by -y , then curve is symmetrical in opposite quadrant .
4 . If x and y are interchanged and equation of curve remains unchanged curve is symmetrical about line y = x .
Nature of Origin 5 . If point ( 0 , 0 ) satisfies the equation , then curve passes through origin .
6 . If curve passes through origin , then equate low st degree term to zero and get equation of tangent . If there are two tangents , then origin is a double point .
Point of Intersection with Axes
7 . Put y = 0 and get intersection with X-axis , put x = 0 and get intersection with Y-axis .
8 . Now , find equation of tangent at this point i . e . , shift origin to the point of intersection and equate the lowest degree term to zero .
9 . Find regions where curve does not exists . i . e ., curve will not exit for those values of variable when makes the other imaginary or not defined .