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
The locus of the point which moves so that the lengths of the tangents from it to two given concentric circles x2 + y2 =...The length of the common chord of circle x2 + y2 − 6x − 16 = 0 and x2 + y2 − 8y − 9 = 0 is-...For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among ...In the argand plane the inequality |(√3 + i)z - (√2 - i)|2 + |(√ + i)z + (√3 - i) |2...Let a circle of radius 4 pass through the origin O , the points $A( - \sqrt{3}a,0)$ and $B(0, - \sqrt{2}\text{ }b)$, whe...