Standard Equation of The Parabola
Category : JEE Main & Advanced
Let S be the focus, \[ZZ'\] be the directrix of the parabola and \[(x,y)\] be any point on parabola, then standard form of the parabola is \[{{y}^{2}}=4ax\].
Some other standard forms of parabola are
(i) Parabola opening to left i.e, \[{{y}^{2}}=-4ax\]
(ii) Parabola opening upwards i.e., \[{{x}^{2}}=4ay\]
(iii) Parabola opening downwards i.e., \[{{x}^{2}}=-4ay\]
Some terms related to parabola
| Important terms | \[{{y}^{2}}=\mathbf{4}ax\] | \[{{y}^{2}}=-\mathbf{4}ax\] | \[{{x}^{2}}=\mathbf{4}ay\] | \[{{x}^{2}}=-\mathbf{4}ay\] |
| Vertex | (0, 0) | (0, 0) | (0, 0) | (0, 0) |
| Focus | \[(a,\text{ }0)\] | \[(-a,\text{ }0)\] | \[(0,\,\,a)\] | \[(0,\,\,-a)\] |
| Directrix | \[x=-a\] | \[x=a\] | \[y=-a\] | \[y=a\] |
| Axis | \[y=0\] | \[y=0\] | \[x=0\] | \[x=0\] |
| Latusrectum | \[4a\] | \[4a\] | \[4a\] | \[4a\] |
| Focal distance \[P(x,y)\] | \[x+a\] | \[a-x\] | \[y+a\] | \[a-y\] |
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