Question

Tangents are drawn from the points on the line $2x-y+3=0$ to the parabola $y^2=4x$. Then the variable chords of contact pass through a fixed point whose coordinates is

• A. $(\frac{3}{2},1)$
• B. $(\frac{5}{2},1)$
• C. $(3,2)$
• D. $(4,3)$

Answer 1

The correct option is A $(\frac{3}{2},1)$

Assuming a point on the line as $(t,2t+3)$
Equation of the chord of contact on the parabola wiil be,
$T=0\Rightarrow y(2t+3)=2(x+t)\Rightarrow (2y-2)t+3y-2x=0\Rightarrow 2y-2=0\text{and}3y=2x\Rightarrow y=1\Rightarrow x=\frac{3}{2}$

Hence the coordinates will be $(\frac{3}{2},1)$