Home
Class 12
MATHS
From the variable point A on circle x^2+...

From the variable point `A` on circle `x^2+y^2=2a^2,` two tangents are drawn to the circle `x^2+y^2=a^2` which meet the curve at `B and Cdot` Find the locus of the circumcenter of ` A B Cdot`

Text Solution

Verified by Experts

The correct Answer is:
`x^(2)+y^(2)=(a^(2))/(2)`
Clearly, `x^(2)+y^(2)=2a^(2)` is director circle of the circle `x^(2)+y^(2)=a^(2)`.
Hence, in the diagram , ABOC is a square and circumcenter P(h,k) of `Delta ABC` is the midpoint of OA.
Hence,
`sqrt(h^(2)+k^(2))=(sqrt(2)a)/(2)`
or the locus is
`x^(2)+y^(2)=(a^(2))/(2)`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 4.18|1 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 4.19|1 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 4.13|4 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at A and B . The locus of the point of intersection of tangents at A and B to the circle x^2+y^2=9 is (a) x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 (c) y^2-x^2=((27)/7)^2 (d) none of these

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

From the origin, chords are drawn to the circle (x-1)^2 + y^2 = 1 . The equation of the locus of the mid-points of these chords

The tangent at any point P on the circle x^(2)+y^(2)=2 , cuts the axes at L and M. Find the equation of the locus of the midpoint L.M.

Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that A B=B C=r . Find the locus of the point of intersection of tangents at Aa n dCdot

Tangents are drawn to the circle x^2+y^2=4 from P(3,4) to touch it at A and B. The parallelogram PAQB is completed. Find the locus of f the point Q.

Through a fixed point (h, k) secants are drawn to the circle x^2 +y^2 = r^2 . Then the locus of the mid-points of the secants by the circle is

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.

Obtain the locus of the point of intersection of the tangent to the circle x^2 + y^2 = a^2 which include an angle alpha .