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.
Radius of one of the circles is

A

`(sqrt(a)-sqrt(beta))^(2)`

B

`(sqrt(alpha)+sqrt(beta))^(2)`

C

`alpha +beta -sqrt(alpha beta)`

D

`alpha +beta -sqrt(2alpha beta)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let equation of circle be `(x-r)^(2) + (y-r)^(2) = r^(2)`
`rArr x^(2) +y^(2) -2r (x+y) +r^(2) =0`, where r is radius of circle which is passing through `(alpha, beta)` so
`alpha^(2) + beta^(2) -2r (alpha +beta) +r^(2) =0`
`rArr r = (2(alpha+beta)+-sqrt(4(alpha+beta)^(2)-4(alpha^(2)+beta^(2))))/(2)`
`rArr r = (alpha + beta) +- sqrt(2 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. Equation of common chord of two 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

Circle K is inscribed in the first quadrant touching the circle radius of the circle K, is-

P(a,5a) and Q(4a,a) are two points. Two circles are drawn through these points touching the axis of y. Centre of these circles are at

Equation of the circle of radius 5 which touches both the coordinate axes is

The circle that can be drawn to touch the coordinate axes and the line 4x + 3y =12 cannot lie in

Find the differential equation of all the 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