Home
Class 12
MATHS
Let P(alpha,beta) be a point in the firs...

Let `P(alpha,beta)` be a point in the first quadrant. Circles are drawn through P touching the coordinate axes.
Equation of common chord of two circles is

A

`x +y = alpha - beta`

B

`x +y = 2 sqrt(alpha beta)`

C

`x +y = alpha +beta`

D

`alpha^(2) -beta^(2) = 4 alpha beta`

Text Solution

Verified by Experts

The correct Answer is:
C
`S_(1) = x^(2) +y^(2) - 2r_(i)(x+y) +r_(i)^(2) =0`, where `i =1,2`
Thus, equation of common chord.
`2(r_(2)-r_(1)) (r+y) +r_(1)^(2) -r_(2)^(2) =0`
`rArr 2(x+y) = (r_(1)+r_(2)) = 2 (alpha + beta)`
`rArr x +y = alpha + beta`.
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    CENGAGE|Exercise Single Correct Answer Type|58 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CIRCLE

    CENGAGE|Exercise JEE Advanced (Single Correct Answer Type)|14 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Question Bank|30 Videos

Similar Questions

Explore conceptually related problems

Let P(alpha,beta) be a point in the first quadrant. Circles are drawn through P touching the coordinate axes. Radius of one of the circles is

P(a,b) is a point in the first quadrant Circles are drawn through P touching the coordinate axes such that the length of common chord of these circles is maximum,if possible values of (a)/(b) is k_(1) and k_(2), then k_(1)+k_(2) is equal to

A is a point (a,b) in the first quadrant.If the two circles which passes through A and touches the coordinate axes cut at right angles then:

P(a,b) is a point in first quadrant.If two circles which passes through point P and touches both the coordinate axis,intersect each other orthogonally,then

The equation of the circle of radius 5 and touching the coordinates axes in third quadrant, is

Find the differential equation of all the circles in the first quadrant which touch the coordinate axes.

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

The differential equation of all circles in the first quadrant which touch the coordiante axes is of order

The equation of the circle whose diameter is common chord to the circles

From the differential equation of the family of all circles in first quadrant and touching the coordinate axes.