Question

Tangents are drawn from the points on the line $x-y+3=0$ to parabola $y^2=8x.$ Then the variable chords of contact pass through a fixed point whose coordinates are

• A. $(3,2)$
• B. $(2,4)$
• C. $(3,4)$
• D. $(4,1)$

Answer 1

The correct option is C $(3,4)$

Let $(k,k+3)$ be the point on the line $x-y+3=0$

Equation of chord of contact is $S_1=0$

$\Rightarrow y{y}_1=4(x+x_1)$

$\Rightarrow y(k+3)=4(x+k)$

$\Rightarrow 4x-3y-k(y-4)=0$

Therefore, straight line passes through fixed point $(3,4)$
Ans: C