the other hand, still using for the equation for becomes or which is false. is not in so it is not in the intersection. The intersection of and can be found by solving the simultaneous equations: Traditional methods for finding intersections include substitution and elimination. Substitution: Solve the first equation for in terms of and then substitute the expression for into the second equation: We then substitute this value for into the other equation and proceed to solve for : Next, we place this value of in either of the original equations and solve for : So our intersection has two points: Elimination: Add (or subtract) a multiple of one equation to the other equation so that one of the variables is eliminated. For our current example, if we subtract the first equation from the second we get . The in the first equation is subtracted from the in the second equation leaving no term. The variable has been eliminated. We then solve the remaining equation for , in the same way as in the substitution method: We then place this value of in either of the original equations and solve for : So our intersection has two points: For conic sections, as many as 4 points might be in the intersection. Finding intercepts One type of intersection which is widely studied is the intersection of a geometric object with the and coordinate axes. The intersection of a geometric object and the -axis is called the -intercept of the object. The intersection of a geometric object and the -axis is called the -intercept of the object. For the line , the parameter specifies the point where the line crosses the axis. Depending on the context, either or the point is called the -intercept. Geometric axis Axis in geometry is the perpendicular line to any line, object or a surface. Also for this may be used the common language use as a: normal (prependicular) line, otherwise in engineering as axial line. In geometry, a normal is an object such as a line or vector that is perpendicular to a given object. For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point. In the three-dimensional case a surface normal, or simply normal, to a surface at a point P is a vector