Home
Class 12
MATHS
The locus of the centres of the circles,...

The locus of the centres of the circles, which touch the circle, ` x^(2)+y^(2)=1` externally, also touch the Y-axis and lie in the first quadrant, is

A

`y=sqrt(1+2x,)xge0`

B

`y=sqrt(1+4x,)xge0`

C

`y=sqrt(1+2y,)yge0`

D

`y=sqrt(1+4y,)yge0`

Text Solution

Verified by Experts

The correct Answer is:
A
Let (h,k) be the centre of the circle and radius r = h as circle touch the Y-axis and other circle `x^(2)+y^(2) = 1` whose centre (0,0) and radius is 1.

`therefore OC = r + 1`
[`therefore` if circles touch each other externally, then `C_(1)C_(2)=r_(1)+r_(2)`]
`rArr sqrt(h^(2)+k^(2))=h+1, hgt0`
and `kgt0`, for first quadrant.
`rArr h^(2)+k^(2)=h^(2)+2h+1`
`rArr k^(2)=2h+1`
`rArrk=sqrt(1+2h), as kgt0`
Now, on taking locus of centre (h,k),we get
`y = sqrt(1+2x),xge0`
Promotional Banner

Similar Questions

Explore conceptually related problems

The locus of the centres of circles which touches (y-1)^(2)+x^(2)=1 externally and also touches X-axis is

The centres of those circles which touch the circle, x^2+y^2-8x-8y-4=0 , externally and also touch the x-axis, lie on : (1) a circle. (2) an ellipse which is not a circle. (3) a hyperbola. (4) a parabola.

Consider the locus of center of the circle which touches the circle x^(2)+y^(2)=4 externally and the line x=4. The distance of the vertex of the locus from the otigin is __________ .

The locus of the centre of a circle the touches the given circle externally is a _______

The locus of the centre of a circle which touches externally the circle x^2 + y^2-6x-6y+14 = 0 and also touches Y-axis, is given by the equation (a) x^2-6x-10y+14 = 0 (b) x^2-10x-6y + 14 = 0 (c) y^2+6x-10y+14-0 (d) y^2-10x-6y + 14 = 0

Prove that the locus of the center of the circle which touches the given circle externally and the given line is a parabola.

The locus of the point (h,k) for which the line hx+ky=1 touches the circle x^2+y^2=4

The locus of the centre of a circle which touches the circle |z-z_(1)|=a " and "|z-z_(2)|=b externally (z, z_(1)" and "z_(2) are complex numbers) will be

The minimum area of circle which touches the parabolas y=x^(2)+1andy^(2)=x-1 is

Find the equation of a circle with center (4, 3) touching the circle x^2+y^2=1