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.
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