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Find pole of line lx+my+n=0 wrt parabola y²=4ax .1.n/l,2am/l2.n/l,-2am/l3.-n/l,2am/l4.-n/l,-2am/l

Find pole of line lx+my+n=0 wrt parabola y²=4ax .1.n/l,2am/l2.n/l,-2am/l3.-n/l,2am/l4.-n/l,-2am/l

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1 Answers

Samyak Jain
333 Points
5 years ago
To find : Pole of line lx+my+n=0 wrt parabola y²=4ax.Sol. Let the pole be (p, q).Equation of polar of (p, q) wrt y²=4ax is T = 0, which isqy = 4a(x + p)/2 i.e. 2ax – qy + 2ap = 0 ....(1)Given eqn of polar is lx+my+n=0. ....(2)Comparing (1) & (2), we get2a = l , –qy = m , 2ap =nSo, lp = n i.e. p = n/lq = –m = –m (l/l) = –m(2a)/lThus, the pole is (n/l,-2am/l)

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