ParabolaHard
Question
From the focus of the parabola y2 = 8x as centre, a circle is described so that a common chord of the curves is equidistant from the vertex and focus of the parabola. The equation of the circle is -
Options
A.(x - 2)2 + y2 = 3
B.(x - 2)2 + y2 = 9
C.(x + 2)2 + y2 = 9
D.x2 + y2 - 4x = 0
Solution
Focus of parabola y2 = 8x is (2, 0). Equation of circle with centre (2, 0) is
(x - 2)2 + y2 = r2
AB is common chord
Q is mid point i.e. (1, 0)
AQ2 = y2 where y2 = 8 × 1 = 8
∴ r2 = AQ2 + QS2 = 8 + 1 = 9
so circle is (x - 2)2 + y2 = 9
Create a free account to view solution
View Solution FreeMore Parabola Questions
The axis of a parabola is along the line y = x and the distance of its vertex from origin is √2 and that from its ...A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is...The co-ordinates of a point on the parabola 2y = x2 which is nearest to the point (0, 3) is...TP & TQ are tangents to the parabola, y2 = 4ax at P & Q. If the chord PQ passes through the fixed point (-a, b) then the...If (t2, 2t) is one end of a focal chord of the parabola y2 = 4x then the length of the focal chord will be -...