Let C be the circle with centre at (1, 1) and | vedclass

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

Question

(B) Let the radius of circle $T$ be $r$. Since $T$ is centered at $(0, y)$ and passes through the origin $(0, 0)$,its radius $r$ is the distance betwe

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(B) Let the radius of circle $T$ be $r$. Since $T$ is centered at $(0, y)$ and passes through the origin $(0, 0)$,its radius $r$ is the distance between $(0, y)$ and $(0, 0)$,so $r = |y|$.Given that $T$ touches circle $C$ externally,the distance between their centers must be equal to the sum of their radii.The center of $C$ is $(1, 1)$ and its radius is $R = 1$.The center of $T$ is $(0, y)$ and its radius is $r = y$ (assuming $y > 0$).The distance between centers $(1, 1)$ and $(0, y)$ is $\sqrt{(1-0)^2 + (1-y)^2} = \sqrt{1 + (1-y)^2}$.Equating this to the sum of radii $R + r = 1 + y$,we get:$\sqrt{1 + (1-y)^2} = 1 + y$Squaring both sides:$1 + (1 - 2y + y^2) = (1 + y)^2$$2 - 2y + y^2 = 1 + 2y + y^2$$2 - 2y = 1 + 2y$$4y = 1$$y = \frac{1}{4}$Thus,the radius of $T$ is $\frac{1}{4}$.

Let $C$ be the circle with centre at $(1, 1)$ and radius $= 1$. If $T$ is the circle centred at $(0, y)$,passing through the origin and touching the circle $C$ externally,then the radius of $T$ is equal to:

Similar Questions

The line $y=mx+c$ intersects the circle $x^2+y^2=r^2$ at two distinct points if:

If the parametric values of two points $A$ and $B$ on the circle $x^2+y^2-6x+4y-12=0$ are $30^{\circ}$ and $90^{\circ}$ respectively,then the equation of chord $AB$ is

If the points $(2, 0), (0, 1), (4, 5)$ and $(0, c)$ are concyclic,then $c$ is equal to

The centre of the circle that passes through the point $(0,1)$ and touches the curve $y=x^2$ at $(2,4)$ is

Let $PQ$ and $RS$ be tangents at the extremities of a diameter $PR$ of a circle of radius $r$ such that $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then $2r$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module