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

Answer: (D)

8

Answer 2

Both point A(1,3),B(1,−1) lies on the parabola y2−2y−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