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
If a circle passing through the point (−1, 0) touches y-axis at (0, 2), then the length of the chord of the circle...The number of tangents that can be drawn from the point (8, 6) to the circle x2 + y2 _ 100 = 0 is...The length of the common chord of the circle x2 + y2 + 4x + 6y + 4 = 0 and x2 + y2 + 6x + 4y + 4 = 0 is-...Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin a...If the line (x + g) cos θ + (y + f) sin θ = k touches the circle x2 + y2 + 2gx + 2fy + c = 0, then -...