The range of values of a such that the angle | vedclass

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

Question

(D) Let the circle be $x^2 + y^2 = 1$. The radius $r = 1$ and the center is $(0, 0)$.Let the point be $P(a, 0)$. The distance from the center to $P$ i

Vedclass · Accepted Answer

$(-\sqrt{2}, -1) \cup (1, \sqrt{2})$

Vedclass · Answer

(D) Let the circle be $x^2 + y^2 = 1$. The radius $r = 1$ and the center is $(0, 0)$.Let the point be $P(a, 0)$. The distance from the center to $P$ is $d = |a|$.Let $	heta$ be the angle between the tangents. Then $\sin(	heta/2) = \frac{r}{d} = \frac{1}{|a|}$.Given $\frac{\pi}{2} Taking the sine function,since $\sin(x)$ is increasing in this interval,we get $\sin(\frac{\pi}{4}) This implies $\frac{1}{\sqrt{2}} Taking the reciprocal,we get $1 This means $|a| > 1$ and $|a| Thus,$a \in (-\sqrt{2}, -1) \cup (1, \sqrt{2})$.

The range of values of $a$ such that the angle $\theta$ between the pair of tangents drawn from the point $(a, 0)$ to the circle $x^2 + y^2 = 1$ satisfies $\frac{\pi}{2} < \theta < \pi$ is :

Similar Questions

The line $2x - y + 1 = 0$ is tangent to the circle at the point $(2, 5)$ and the centre of the circle lies on $x - 2y = 4$. The radius of the circle is

$A$ common tangent to the circle $x^2+y^2=9$ and parabola $y^2=8x$ is

Two tangents $PQ$ and $PR$ are drawn to the circle $x^2 + y^2 - 2x - 4y - 20 = 0$ from the point $P(16, 7)$. If the centre of the circle is $C$,then the area of quadrilateral $PQCR$ is ............ $sq. \text{ units}$.

$A$ straight line passing through the point $(1,0)$ and not parallel to the $x$-axis intersects the curve $2x^2+5y^2-7x=0$ at two points $A$ and $B$. The angle subtended by the line segment $AB$ at the origin is (in $^\circ$)

Let $AB$ be a chord of the circle $x^2 + y^2 = r^2$ subtending a right angle at the centre. Then the locus of the centroid of the $\Delta PAB$ as $P$ moves on the circle is

Vedclass Test Series

Exam Paper Generator

Online Exam Module