Question

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

• A. 4
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (D)

Both point $A(1,3),B(1,-1)$ lies on the parabola
$y^2-2y-2x-1=0$
Fquation 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 $(-3,1)$
$\Rightarrow A=\frac{1}{2}\left|\begin{array}{ccc}1& 3& 1\\ 1& -1& 1\\ -3& 1& 1\end{array}\right|=8$