The area of the triangle formed by the positive x-axis and the normal and tangent to the circle x2+y2=4 at (1, √3) is

Question

The area of the triangle formed by the positive x-axis and the normal and tangent to the circle x2+y2=4 at (1, √3) is (A) 2 √3 sq. units (B) 3 √2 sq. units (C) √6 sq. units (D) none of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/305be98c6003c85cbcd8fca74260390d-.png" /> The equations of the tangent and the normal to x2+y2=4 at (1, √3) are, respectively, x+√3 y=4 and y=√3 x The tangent meets the x-axis at (4,0). Therefore, Area of triangle O A P=(1/2)(4) √3 =2 √3 sq. units

Q. The area of the triangle formed by the positive $x$ -axis and the normal and tangent to the circle $x^{2} + y^{2} = 4$ at $(1, 3)$ is

$23$ sq. units

$32$ sq. units

$6$ sq. units

none of these

The equations of the tangent and the normal to
$x^{2} + y^{2} = 4$ at $(1, 3)$ are, respectively,
$x + 3 y = 4$ and $y = 3 x$
The tangent meets the $x$ -axis at $(4, 0)$ . Therefore,
Area of $△ O A P = \frac{1}{2} (4) 3$
$= 23$ sq. units

Q. The area of the triangle formed by the positive x-axis and the normal and tangent to the circle x2+y2=4 at (1,3​) is

23​ sq. units

32​ sq. units

6​ sq. units