The number of common tangents to the circles | vedclass

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

Question

(C) For the first circle $x^2 + y^2 = 1$,the center $C_1 = (0, 0)$ and radius $r_1 = 1$.For the second circle $x^2 + y^2 - 4x + 3 = 0$,we rewrite it a

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) For the first circle $x^2 + y^2 = 1$,the center $C_1 = (0, 0)$ and radius $r_1 = 1$.For the second circle $x^2 + y^2 - 4x + 3 = 0$,we rewrite it as $(x-2)^2 + y^2 = 1$,so the center $C_2 = (2, 0)$ and radius $r_2 = 1$.The distance between the centers $C_1$ and $C_2$ is $d = \sqrt{(2-0)^2 + (0-0)^2} = 2$.Since $d = r_1 + r_2 = 1 + 1 = 2$,the two circles touch each other externally.When two circles touch externally,the number of common tangents is $3$.

The number of common tangents to the circles $x^2 + y^2 = 1$ and $x^2 + y^2 - 4x + 3 = 0$ is

Similar Questions

The equation of the pair of straight lines parallel to the $x$-axis and touching the circle $x^2+y^2-6x-4y-12=0$ is

The circle $x^2+y^2+4x-4y+4=0$ touches...

The equation of the circle which passes through $(1, 0)$ and $(0, 1)$ and has its radius as small as possible,is

If a circle $C$ passing through the point $(4, 0)$ touches the circle $x^2+y^2+4x-6y=12$ externally at the point $(1, -1)$,then the radius of $C$ is

The circle $x^2 + y^2 - 4x - 4y + 4 = 0$ is...

Vedclass Test Series

Exam Paper Generator

Online Exam Module