The area (in sq units) of the triangle formed | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The equation of the circle is $x^2+y^2=4$. The point $P(1, \sqrt{3})$ lies on the circle.The equation of the tangent at $P(x_1, y_1)$ is $xx_1 + y

Vedclass · Accepted Answer

$2 \sqrt{3}$

Vedclass · Answer

(C) The equation of the circle is $x^2+y^2=4$. The point $P(1, \sqrt{3})$ lies on the circle.The equation of the tangent at $P(x_1, y_1)$ is $xx_1 + yy_1 = r^2$,which is $x(1) + y(\sqrt{3}) = 4$,or $x + \sqrt{3}y = 4$.The tangent meets the $X$-axis at $A(4, 0)$.The normal at $P(1, \sqrt{3})$ passes through the origin $O(0, 0)$ and has the equation $y = \sqrt{3}x$.The triangle is formed by the points $O(0, 0)$,$P(1, \sqrt{3})$,and $A(4, 0)$.The area of $	riangle OPA = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes OA 	imes y_P = \frac{1}{2} 	imes 4 	imes \sqrt{3} = 2 \sqrt{3}$ sq units.

The area (in sq units) of the triangle formed by the tangent,normal at $(1, \sqrt{3})$ to the circle $x^2+y^2=4$ and the $X$-axis,is

Similar Questions

If the line $y = \sqrt{3}x + k$ touches the circle $x^2 + y^2 = 16$,then $k =$

If the tangent at $(1,7)$ to the curve $x^2=y-6$ touches the circle $x^2+y^2+16x+12y+C=0$,then $C=$

The tangent to the circle $C_1 : x^2 + y^2 - 2x - 1 = 0$ at the point $(2, 1)$ cuts off a chord of length $4$ from a circle $C_2$ whose centre is $(3, -2)$. The radius of $C_2$ is

Suppose two tangents $PA$ and $PB$ are drawn to the circle centered at $C(1, 2)$ from the point $P(16, 7)$. If the area of the quadrilateral $PACB$ is $75$ square units,then the radius of the circle is:

Let the equation of a circle be $x^{2}+y^{2}-6x-4y+9=0$. Then the line $4x+3y-8=0$ is a

Vedclass Test Series

Exam Paper Generator

Online Exam Module