The tangent and normal to the parabola y2=4x at point P(1 , 2) intersects y -axis at point A and B respectively. The area of circumcircle of triangle PAB is

Question

The tangent and normal to the parabola y2=4x at point P(1 , 2) intersects y -axis at point A and B respectively. The area of circumcircle of triangle PAB is (A) π  (B) (π /2) (C) 2π  (D) 4π

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-vbqehlebafhxqaos.jpg" /> T:y=x+1 N:y=-x+3 A≡ (0 , 1)B≡ (0 , 3) AB is diameter ∴ radius =1

Q. The tangent and normal to the parabola $y^{2} = 4 x$ at point $P (1, 2)$ intersects $y$ -axis at point $A$ and $B$ respectively. The area of circumcircle of triangle $P A B$ is

$π$

$\frac{π}{2}$

$2 π$

$4 π$

$T : y = x + 1$
$N : y = - x + 3$
$A \equiv (0, 1) B \equiv (0, 3)$
$A B$ is diameter
$∴$ radius $= 1$

Q. The tangent and normal to the parabola y2=4x at point P(1,2) intersects y -axis at point A and B respectively. The area of circumcircle of triangle PAB is

π

2π​

2π

4π

T:y=x+1 N:y=−x+3 A≡(0,1)B≡(0,3) AB is diameter ∴ radius =1

Q. The tangent and normal to the parabola $y^{2} = 4 x$ at point $P (1, 2)$ intersects $y$ -axis at point $A$ and $B$ respectively. The area of circumcircle of triangle $P A B$ is

$π$

$\frac{π}{2}$

$2 π$

$4 π$

$T : y = x + 1$
$N : y = - x + 3$
$A \equiv (0, 1) B \equiv (0, 3)$
$A B$ is diameter
$∴$ radius $= 1$