Tangents are drawn to the parabola `y^2=4a x` at the point where the line `l x+m y+n=0` meets this parabola. Find the point of intersection of these tangents.

Options

A. `(n,//1, -2am//1)`
B. `(l//n, -2am//n)`
C. `(n//m, -2al//m)`
D. none of these

Answer

A

Explanation

Let the point of intersection of tangents be `(x_(1), y_(1))` then the equation of the chord of contact of tangents drawn from P to the parabola `y^(2)=4ax" is "yy_(1)=2a(x+x_(1))`.
Clearly, lx+my+n=0 is also the chord of contact of tangents.
Therefore, `yy_(1)=2a(x+x_(1))" and "lx+my+n=0` represent the same line.
`:." "(2a)/l=(-y_(1))/m=(2ax_(1))/nrArr=n/l" and "y_(1)=(2am)/l`
Hence, the required point is `(n..l, -2am//l)`