CircleHard
Question
A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is
Options
A.(x - p)2 = 4qy
B.(x - q)2 = 4py
C.(y - p)2 = 4qx
D.(y - q)2 = 4px
Solution
Let the other end of diameter is (h, k) then equation of circle is
(x - h)(x - p) + (y - k)(y - q) = 0
Put y = 0, since x-axis touches the circle
⇒ x2 - (h + p)x + (hp + kq) = 0 ⇒ (h + p)2 = 4(hp + kq) (D = 0)
⇒ (x - p)2 = 4qy.
(x - h)(x - p) + (y - k)(y - q) = 0
Put y = 0, since x-axis touches the circle
⇒ x2 - (h + p)x + (hp + kq) = 0 ⇒ (h + p)2 = 4(hp + kq) (D = 0)
⇒ (x - p)2 = 4qy.
Create a free account to view solution
View Solution FreeMore Circle Questions
The focal chord to y2 = 16x is tangent to (x - 6)2 + y2 = 2, then the possible values of the slope of this chord are:-...Consider the hyperbola 3x2 - y2 - 24x + 4y - 4 = 0 -...Let A be the vertex and L the length of the latus rectum of parabola, y2 - 2y - 4x - 7 = 0.The equation of the parabola ...If the lengths of the tangents drawn from the point (1, 2) to the circles x2 + y2 + x + y − 4 = 0 and 3x2 + 3y2 &#...The equation of circles passing through (3, _6) touching both the axes is...