Pole and Polar
Category : JEE Main & Advanced
The locus of the point of intersection of the tangents to the parabola at the ends of a chord drawn from a fixed point P is called the polar of point P and the point P is called the pole of the polar.
Equation of polar : Equation of polar of the point \[({{x}_{1}},\,{{y}_{1}})\] with respect to parabola \[{{y}^{2}}=4ax\] is same as chord of contact and is given by \[y{{y}_{1}}=2a(x+{{x}_{1}})\].
Coordinates of pole : The pole of the line \[lx+my+n=0\] with respect to the parabola \[{{y}^{2}}=4ax\]is \[\left( \frac{n}{l},\frac{-2am}{l} \right)\].
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