Any circle passing through the point of inter | vedclass

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

Question

(A) Let the two lines be $L_1: x + \sqrt{3}y - 1 = 0$ and $L_2: \sqrt{3}x - y - 2 = 0$.The slopes of these lines are $m_1 = -\frac{1}{\sqrt{3}}$ and $

Vedclass · Accepted Answer

$180$

Vedclass · Answer

(A) Let the two lines be $L_1: x + \sqrt{3}y - 1 = 0$ and $L_2: \sqrt{3}x - y - 2 = 0$.The slopes of these lines are $m_1 = -\frac{1}{\sqrt{3}}$ and $m_2 = \sqrt{3}$.Since $m_1 	imes m_2 = -\frac{1}{\sqrt{3}} 	imes \sqrt{3} = -1$,the lines are perpendicular to each other.Let the point of intersection be $R$. Since the lines are perpendicular,the angle between them at $R$ is $	heta = 90^{\circ}$.In a circle,the angle subtended by an arc at the centre is twice the angle subtended by the same arc at any point on the remaining part of the circle.Therefore,the angle subtended by the arc $PQ$ at the centre is $2 	imes 90^{\circ} = 180^{\circ}$.

Any circle passing through the point of intersection of the lines $x + \sqrt{3}y = 1$ and $\sqrt{3}x - y = 2$ intersects these lines at points $P$ and $Q$. The angle subtended by the arc $PQ$ at its centre is- ............. $^o$

Similar Questions

From the origin,chords are drawn to the circle $(x - 1)^2 + y^2 = 1$. The locus of the midpoints of these chords is a

Two perpendicular tangents to the circle $x^2 + y^2 = a^2$ meet at point $P$. The equation of the locus of $P$ is:

$A$ point moves such that its distance from the point $(-1, 0)$ is always three times its distance from the point $(0, 2)$. The locus of the point is

Let $A=(2,0)$ and $B=(0,-2)$. Let $P$ be any point such that the sum of the distances of $P$ from $A$ and $B$ is $4$. Then the equation of the locus of the point $P$ is

The locus of the centre of a circle which touches externally the circle $x^2 + y^2 - 6x - 6y + 14 = 0$ and also touches the $y$-axis,is given by the equation

Vedclass Test Series

Exam Paper Generator

Online Exam Module