CircleHard
Question
The centre of a circle passind through the points (0, 0), (1,0) and touching the circle x2 + y2 = 9 is
Options
A.(3 / 2,1/ 2)
B.(1/ 2,3 / 2)
C.(1/ 2,1/ 2)
D.(1/ 2,-21/2)
Solution
Let 1C (h, k) be the required circle. Then
⇒ h2 + k2 = h2 - 2h + 1 + k2
⇒ -2h +1= 0
⇒ h = 1/ 2
Since, (0, 0) and (1, 0) lie inside the circle x2 + y2 = 9
Therefore, the required circle can touch the given circle internally.
ie,C1 . C2 = r1 ~ r2
⇒
⇒
⇒
⇒
⇒
⇒ k2 = 2
⇒
Therefore, (d), is the answer.
⇒ h2 + k2 = h2 - 2h + 1 + k2
⇒ -2h +1= 0
⇒ h = 1/ 2
Since, (0, 0) and (1, 0) lie inside the circle x2 + y2 = 9
Therefore, the required circle can touch the given circle internally.
ie,C1 . C2 = r1 ~ r2
⇒
⇒
⇒
⇒
⇒
⇒ k2 = 2
⇒
Therefore, (d), is the answer.
Create a free account to view solution
View Solution FreeMore Circle Questions
Tangents OP and OQ are drawn from the origin O to the circle x2 + y2 + 2gx + 2fy + c = 0. Then, the equation of the circ...Find the co-ordinates of a point p on line x + y = _ 13, nearest to the circle x2 + y2 + 4x + 6y _ 5 = 0...There equal circles each of radius r touch one another. The radius of the circle touching all the three given circles in...The equation of the circum-circle of the triangle formed by the lines x = 0, y = 0, = 1, is -...The locus of the mid point of the focal radii of a variable point moving on the parabola, y2 = 4ax is a parabola whose...