Home
Class 12
MATHS
The locus of the point at which two give...

The locus of the point at which two given unequal circles subtend equal angles is: (A) a straight line(B) a circle (C) a parabola (D) an ellipse

A

a straihght line

B

a circle

C

a parabola

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B

Let two circles be `S =0` nd `S' =0` having radii `r_(1)` and `r_(2)`. Respectively
From the figure, we have
`(r_(1))/(sqrt(S_(1))) =(r_(2))/(sqrt(S'_(1)))`
`rArr S'_(1) r_(1)^(2) = r_(2)^(2) S_(1)`
`rArr S_(1) - ((r_(1))/(r_(2)))^(2) S'_(1) =0`
`:.` Locus of `P(h,k)`
`S -((r_(1))/(r_(2)))^(2) S' =0`, which represents the equation of a circle,
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|9 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|7 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|9 Videos

Similar Questions

Explore conceptually related problems

The locus of the points of trisection of the double ordinates of the parabola y^2 = 4ax is : (A) a straight line (B) a circle (C) a parabola (D) none of these

Find the locus of the point at which two given portions of the straight line subtend equal angle.

If Re((2z+1)/(iz+1))=1 , the the locus of the point representing z in the complex plane is a (A) straight line (B) circle (C) parabola (D) none of these

The locus of the centre of a circle which touches two given circles externally is a

The locus of the centre of a circle which cuts a given circle orthogonally and also touches a given straight line is (a) circle (c) parabola (b) line (d) ellipse

Consider a curve ax^2+2hxy+by^2=1 and a point P not on the curve. A line drawn from the point P intersect the curve at points Q and R. If he product PQ.PR is (A) a pair of straight line (B) a circle (C) a parabola (D) an ellipse or hyperbola

The locus of the point (sqrt(3h),sqrt(3k+2)) if it lies on the line x-y-1=0 is (a) straight line (b) a circle (c) a parabola (d) none of these

Prove Equal chords of a circle subtend equal angles at the centre.

Prove Equal chords of congruent circles subtend equal angles at the centre.

Prove that equal chords of congruent circles subtend equal angles at their centre.