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.