Question

The pole of the line lx+my+n=0 with respect to the parabola `y^(2)=4ax,` is
A. `(n/l,-(2am)/l)`
B. `(n/m,-(2am)/m)`
C. `(n/m,-(2al)/m)`
D. none of these

Answer 1

Correct Answer - A
Let the pole be `(x_(1), y_(1))`. Then, the equation of the polar with respect to `y^(2)=4ax` is
`yy_(1)=2a(x+x_(1))`
`"or, "2ax-yy_(1)+2ax_(1)=0" ....(i)"`
Clearly, (i) and lx+my+n=0 represent the same line.
`:." "(2a)/l=(-y_(1))/m=(2ax_(1))/nrArrx_(1)n/l" and "y_(1)=-(2am)/l`
Hence, the pole of the given line is `(n/l,-(2am)/l)`