The centre of the smallest circle touching th | vedclass

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

Question

(D) Given circles are:$S_1: x^2 + y^2 - 2y - 3 = 0$Centre $C_1 = (0, 1)$,Radius $r_1 = \sqrt{0^2 + (-1)^2 - (-3)} = \sqrt{1 + 3} = 2$.$S_2: x^2 + y^2

Vedclass · Accepted Answer

$(2, 5)$

Vedclass · Answer

(D) Given circles are:$S_1: x^2 + y^2 - 2y - 3 = 0$Centre $C_1 = (0, 1)$,Radius $r_1 = \sqrt{0^2 + (-1)^2 - (-3)} = \sqrt{1 + 3} = 2$.$S_2: x^2 + y^2 - 8x - 18y + 93 = 0$Centre $C_2 = (4, 9)$,Radius $r_2 = \sqrt{(-4)^2 + (-9)^2 - 93} = \sqrt{16 + 81 - 93} = \sqrt{4} = 2$.Since the radii of both circles are equal $(r_1 = r_2 = 2)$,the smallest circle touching both circles externally will have its diameter equal to the distance between the two circles along the line joining their centres.The centre of this smallest circle is the midpoint of the line segment joining the centres $C_1$ and $C_2$.Midpoint $= \left( \frac{0 + 4}{2}, \frac{1 + 9}{2} \right) = (2, 5)$.

The centre of the smallest circle touching the circles $x^2 + y^2 - 2y - 3 = 0$ and $x^2 + y^2 - 8x - 18y + 93 = 0$ is:

Similar Questions

If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle $60^o$ on the circumference of the first circle,then the radius of the arc is

Three circles of radius $r$ touch each other externally. What is the radius of the circle that touches all three circles internally?

The length of the chord of the circle $x^{2}+y^{2}+3x+2y-8=0$ intercepted by the $y$-axis is

The radical axis of two circles and the line joining their centres are:

Let $P$ and $Q$ be any points on the curves $(x-1)^{2}+(y+1)^{2}=1$ and $y=x^{2}$,respectively. The distance between $P$ and $Q$ is minimum for some value of the abscissa of $P$ in the interval

Vedclass Test Series

Exam Paper Generator

Online Exam Module