Question

The tangents at the point $A (1,3)$ and $B (1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$ Then the area (in unit $^2$ ) of $\triangle PAB$ is :-

• A. 4
• B. 6
• C. 7
• D. 8

Answer 1

The Correct Option is D

Both point $A(1,3),B(1,-1)$ lies on the parabola $y^2-2y-2x-1=0$

Equation of tangent aty $A(1,3)$ is $T=0$
$x-2y+5=0$

and equation of tangent at $B(1,-1)$ is $T=0$
$x+2y+1=0$

⇒So point $P$ is $(-3,1)$

⇒ A = $\frac1{2}$ $ \begin{bmatrix} 1 & 3 & 1 \\ 1 & -1 & 1 \\ -3 & 1 & 1 \end{bmatrix} =8$

Therefore, the correct answer is option (D) : 8