Category : JEE Main & Advanced
(1) Position of a point with respect to a parabola : The point \[P({{x}_{1}},{{y}_{1}})\] lies outside, on or inside the parabola \[{{y}^{2}}=4ax\] according as \[y_{1}^{2}-4a{{x}_{1}}>,=\text{,}\,<0\].
(2) Intersection of a line and a parabola: The line \[y=mx+c\] does not intersect, touches or intersect a parabola \[{{y}^{2}}=4ax\], according as \[c>,=,<\frac{a}{m}\].
Condition of tangency : The line \[y=mx+c\] touches the parabola, if \[c=a/m\].
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