CircleHard
Question
Consider a family of circles which are passing through the point (-1, 1) and are tangent to xaxis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval
Options
A.0 < k < 1/2
B.k ≥ 1/2
C.- 1/2 ≤ k ≤ 1/2
D.k ≤ 1/2
Solution
Equation of circle (x - h)2 + (y - k)2 = k2
It is passing through (- 1, 1) then
(- 1 - h)2 + (1 - k)2 = k2
h2 + 2h - 2k + 2 = 0
D ≥ 0
2k - 1 ≥ 0 ⇒ k ≥ 1/2.
It is passing through (- 1, 1) then
(- 1 - h)2 + (1 - k)2 = k2
h2 + 2h - 2k + 2 = 0
D ≥ 0
2k - 1 ≥ 0 ⇒ k ≥ 1/2.
Create a free account to view solution
View Solution FreeMore Circle Questions
The distance from the centre of the circle x2 + y2 = 2x to the straight line passing through the points of intersection ...Centre of a circle is (2, 3). If the line x + y = 1 touches it. Find the equation of circle-...Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this tr...The area of smaller region bounded by the circle x2 + y2 = 1 and the lines |y| = x + 1 is...If (4, 3) and (−12, −1) are end points of a diameter of a circle, then the equation of the circle is-...