The number of circles touching the lines x = | vedclass

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

Question

(B) Let the circle have center $(h, k)$ and radius $r$.Since the circle touches the lines $y = a$ and $y = b$,the diameter of the circle must be equal

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Let the circle have center $(h, k)$ and radius $r$.Since the circle touches the lines $y = a$ and $y = b$,the diameter of the circle must be equal to the distance between these two parallel lines.Thus,$2r = |b - a|$,which implies $r = \frac{|b - a|}{2}$.The distance from the center $(h, k)$ to the line $y = a$ is $|k - a| = r$,so $k = a \pm r$.The distance from the center $(h, k)$ to the line $x = 0$ is $|h| = r$,so $h = \pm r$.Since $r$ is fixed,for each value of $h$ ($r$ or $-r$),we get a circle. Thus,there are exactly $2$ such circles.

The number of circles touching the lines $x = 0$,$y = a$ and $y = b$ is

Similar Questions

Find the equation of a circle that touches the lines $x = 0$,$y = 0$,and $x = 2c$.

What is the length of the diameter of the circle $x^2 + y^2 - 4x - 6y + 4 = 0$?

Find the equation of a circle whose diameters are $2x - 3y = 5$ and $3x - 4y = 7$ and whose radius is $8$.

The parametric equations of the circle $x^2+y^2+2x-4y-4=0$ are

If four distinct points $(2k, 3k)$, $(2,0)$, $(0,3)$, and $(0,0)$ lie on a circle, then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module