Home
Class 12
MATHS
P(α,β) is a point in first quadrant. If ...

P(α,β) 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

A

A. `alpha^(2) + beta^(2) = 4 alpha beta`

B

B. `(alpha + beta)^(2) = 4 alpha beta`

C

C. `alpha^(2) +beta^(2) = alpha beta`

D

D. `alpha^(2) +beta^(2) = 2 alpha beta`

Text Solution

Verified by Experts

The correct Answer is:
A
For orthogonal of two circle `2(r_(1)-r_(2))^(2) = r_(1)^(2) +r_(2)^(2)`
`rArr (r_(1)+r_(2))^(2) = 6r_(1)r_(2)`
`rArr 4(alpha + beta)^(2) = 6 (alpha^(2)+beta^(2))`
`rArr alpha^(2) + beta^(2) = 4 alpha beta`
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|9 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

P is a point(a,b) in the first quadrant. If the two circles which pass through P and touch both the co-ordinates axes cut at right angles , then

Find the equation of a circle which passes through the point (4, 2) and touches both the coordinate axes. How many such circles are possible?

The two circles which passes through (0,a) and (0,-a) and touch the line y = mx+c will intersect each other at right angle ,if

P is a point inside a circel: NO tangent of the circle will pass through P.

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

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

The tangent to a circle and the radius passing through the point of contact are perpendicular to each other.

P and Q are two points ona circle with centre at O. R is a point on the minor arc of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet each other at the points S. If anglePSQ =20^@ , then anglePRQ =

A variable circle passes through the fixed point A(p,q) and touches the x-axis. The locus of the other end of the diameter through A is-

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