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

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

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 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

The sum of the intercepts cut off from the axes of coordinates by a variable straight line is 10 units . Find the locus of the point which divides internally the part of the straight line intercepted between the axes of coordinates in the ratio 2:3 .

A moving straight line always passes through the point (h,k) . Prove that the locus of the middle point of the portion of the straight line intercepted between the axes of coordinates is , (h)/(x)+(k)/(y)=2 .

The sum of the intercepts cut off from the coordinate axes by a variable line is 14 units . Find the locus of the point which divides internally the portion of the line intercepted between the coordinate axes in the ratio 3:4 .

A line of fixed length a+b moves so that its ends are always on two fixed perpendicular straight lines. Then the locus of the point which divides this line into portions of length aa n db is (a) an ellipse (b) parabola (c) straight line (d) none of these

Find the locus of the midpoint of the chords of the parabola y^2=4ax .which subtend a right angle at the vertex.

Find the coordinates of the middle point of the portion of the straight line 2x+y=4 intercepted between the x and the y - axes.

The numberical value of the area of the triangle formed by a moving line on the coordinate axes is 2c^(2) . Find the locus of the middle point of the portion of the line intercepted between the axes.

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

Find the locus of the mid point of the chord of the circle x^2+y^2=a^2 which subtend a right angle at the point (0,0).

Find the locus of the foot of the perpendicular drawn from the origin to the straight line which passes through the fixed point (a,b).