Home
Class 12
MATHS
If the radius of the circle touching the...

If the radius of the circle touching the pair of lines `7x^(2) - 18 xy +7y^(2) = 0` and the circle `x^(2) +y^(2) - 8x - 8y = 0`, and contained in the given circle is equal to k, then `k^(2)` is equal to

A

10

B

9

C

8

D

7

Text Solution

Verified by Experts

The correct Answer is:
C

`tan theta = |(2sqrt(h^(2)-ab))/(a+b)| =(4sqrt(2))/(7)`
`:. tan. (theta)/(2) = (1)/(2sqrt(2))`
`:. sin .(theta)/(2) = (1)/(3) = (sqrt(2)(8-alpha))/(sqrt(2)alpha)`
`:. alpha = 6`
Hence, equation of circle is `(x-6)^(2) +(y-6)^(2) = 8`.
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 circle x ^(2) +y^(2) -8 x+4=0 touches -

The circle x^2 + y^2 - 8x + 4y +4 = 0 touches

The equation of a circle of radius 1 touching the circle x^2 + y^2 - 2|x| = 0 is

The straight line x+y - 1= 0 cuts the circle x^(2) + y^(2) - 6x - 8y = 0 at A and B. Find the equation of the circle of which AB is a diameter.

Equation of the circles concentric with the circle x^(2)+y^(2)-2x-4y=0 and touching the circle x^(2)+y^(2)+ 2x=1 must be-

The point (2, -1) ________ the circle x^(2) + y^(2) - 4x + 6y + 8 = 0 .

Find the equation to the circle described on the common chord of the given circles x^(2) + y^(2) - 4x - 5 = 0 and x^(2) + y^(2) + 8x + 7 = 0 as diameter.

The ordinate of the centre of the circle passing through (0,0) and (1,0) and touching the circle x ^(2) + y^(2) =9 is-

Find the equation to the common chord of the two circles x^(2) + y^(2) - 4x + 6y - 36 = 0 and x^(2) + y^(2) - 5x + 8y - 43 = 0 .

State which of the following is the radius of the circle x^(2) + y^(2) + 4x - 8y - 5 = 0 ?