The point at which the circles x^2+y^2-4x-4y+ | vedclass

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

Question

(C) The given circles are $S_1: x^2+y^2-4x-4y+7=0$ and $S_2: x^2+y^2-12x-10y+45=0$.For $S_1$,the centre $C_1 = (2, 2)$ and radius $r_1 = \sqrt{2^2+2^2

Vedclass · Accepted Answer

$\left(\frac{14}{5}, \frac{13}{5}\right)$

Vedclass · Answer

(C) The given circles are $S_1: x^2+y^2-4x-4y+7=0$ and $S_2: x^2+y^2-12x-10y+45=0$.For $S_1$,the centre $C_1 = (2, 2)$ and radius $r_1 = \sqrt{2^2+2^2-7} = \sqrt{8-7} = 1$.For $S_2$,the centre $C_2 = (6, 5)$ and radius $r_2 = \sqrt{6^2+5^2-45} = \sqrt{36+25-45} = \sqrt{16} = 4$.The distance between the centres $C_1C_2 = \sqrt{(6-2)^2+(5-2)^2} = \sqrt{4^2+3^2} = \sqrt{16+9} = 5$.Since $C_1C_2 = r_1+r_2 = 1+4 = 5$,the circles touch each other externally.The point of contact $P$ divides the line segment $C_1C_2$ internally in the ratio $r_1:r_2 = 1:4$.Using the section formula,$P = \left(\frac{1(6)+4(2)}{1+4}, \frac{1(5)+4(2)}{1+4}\right) = \left(\frac{6+8}{5}, \frac{5+8}{5}\right) = \left(\frac{14}{5}, \frac{13}{5}\right)$.

The point at which the circles $x^2+y^2-4x-4y+7=0$ and $x^2+y^2-12x-10y+45=0$ touch each other is:

Similar Questions

$M_p$ denotes the mass of a proton and $M_n$ denotes the mass of a neutron. $A$ given nucleus,of binding energy $B$,contains $Z$ protons and $N$ neutrons. The mass $M(N, Z)$ of the nucleus is given by ($c$ is the velocity of light):

If $\frac{x^2+x+1}{x^2+2x+1} = A + \frac{B}{x+1} + \frac{C}{(x+1)^2}$,then $A-B$ is equal to

The molecular interactions responsible for hydrogen bonding in $HF$ are:

Let $a \neq 0$ and $p(x)$ be a polynomial of degree greater than $2$. If $p(x)$ leaves remainders $a$ and $-a$ when divided respectively by $x+a$ and $x-a$,then the remainder when $p(x)$ is divided by $x^2-a^2$ is:

If $\cos 2x = (\sqrt{2} + 1) \left(\cos x - \frac{1}{\sqrt{2}}\right)$ and $\cos x \neq \frac{1}{\sqrt{2}}$,then $x \in$

Vedclass Test Series

Exam Paper Generator

Online Exam Module