Home
Class 12
MATHS
The locus of the center of a variable ci...

The locus of the center of a variable circle which always touches two given circles externally is

Text Solution

Verified by Experts

As shown in the figure, variable circle S with centre C and radius r touches two given disjoint circles `S_(1)` and `S_(2)` having centres `C_(1)` and `C_(2)` and radii `r_(1)` and `r_(2)`, respectively.

Clearly, `"CC"_(1)=r+r_(1) and "CC"_(2)=r+r_(2)`
`therefore" CC"_(1)-"CC"_(2)=r_(1)-r_(2)(="constant")`
Thus, locus of centre C is hyperbola having foci `C_(1) and C_(2)`.
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES|11 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.1|3 Videos

  • HIGHT AND DISTANCE

    CENGAGE PUBLICATION|Exercise Archives|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|2 Videos

Similar Questions

Explore conceptually related problems

Two circles are given such that they neither intersect nor touch. Then identify the locus of the center of variable circle which touches both the circles externally.

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

Two circles are given such that one is completely lying inside the other without touching. Prove that the locus of the center of variable circle which touches the smaller circle from outside and the bigger circle from inside is an ellipse.

The locus of the centres of the circles which touch both the axes is given by

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 which touches the circles |z-z_(1)|=a and |z-z_(2)|=b externally (z, z_(1), z_(2) are complex numbers) will be-

The locus of the centre of a circle which passes through two variable points (a, 0), (-a, 0) is:

The locus of the centre of a circle which passes through two variable points (a, 0), (-a, 0) is

Find the locus of the center of the circle touching the circle x^2+y^2-4y-2x=4 internally and tangents on which from (1, 2) are making of 60^0 with each other.