Home
Class 12
MATHS
x^2 +y^2 = 16 and x^2 +y^2=36 are two ci...

`x^2 +y^2 = 16 and x^2 +y^2=36` are two circles. If `P and Q` move respectively on these circles such that `PQ=4` then the locus of mid-point of `PQ` is a circle of radius

A

`sqrt(20)`

B

`sqrt(22)`

C

`sqrt(30)`

D

`sqrt(32)`

Text Solution

Verified by Experts

The correct Answer is:
B
Using Apollonius theorem in `DeltaPCQ`, we get

`CP^(2) + CQ^(2) = 2(CR^(2) +RQ^(2))`
`rArr 16 + 36 =2 (CR^(2) + ((4)/(2))^(2))`
`rArr 52 = 2(CR^(2) +4)`
`rArr CR = sqrt(22)`
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|9 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise For problems 3 and 4|2 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

Similar Questions

Explore conceptually related problems

If the line hx+ky=1 touches x^2+y^2=a^2 , then the locus of the point (h,k) is a circle of radius

Let P be the point (1,0) and Q a point on the parabola y^(2) =8x, then the locus of mid-point of bar(PQ is-

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x . The locus of the midpoint of PQ is

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

The centres of a set of circles, each of radius 3 , lie on the circle x^2+y^2=25 . The locus of any point in the set is

x+y=6 and x+2y=4 are two diameters of a circle. If the circel passes through the point (6,2), then its radius is-

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

PQ is a chord of the parabola y^(2) = 4ax . The ordinate of P is twice that of Q . Prove that the locus of the mid - point of PQ is 5y^(2) = 18 ax

Let C_(1) and C_(2) denote the centres of the circles x^(2) +y^(2) = 4 and (x -2)^(2) + y^(2) = 1 respectively and let P and Q be their points of intersection. Then the areas of triangles C_(1) PQ and C_(2) PQ are in the ratio _