CircleHard

Question

Locus of the image of the point (2, 3) in the line (2x − 3y + 4) + k (x − 2y + 3) = 0, k ∈R, is a

Options

A.circle of radius √2
B.circle of radius √3
C.straight line parallel to x-axis
D.straight line parallel to x-axis

Solution


P is the fixed point for given family of line PB = PA ⇒ (α − 1)2 + (α − 2)2 = 1 + 1 (x − 1)2 + (y − 2)2 = (√2)2
∴locus is a circle of radius 2

Create a free account to view solution

View Solution Free
Topic: Circle·Practice all Circle questions

More Circle Questions

If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is 3x + 4y + 3 = 0, then theequati...The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the x-axis in points whose abscissa ...If y + 3x = 0 is the equation of a chord of the circle, x2 + y2 − 30x = 0, then the equation of the circle with th...A variable circle is drawn to touch the x-axis at the origin. The locus of the pole of the straight line lx + my + n = 0...The equation of the circle whose diameter is the common chord of the circles x2 + y2 + 3x + 2y + 1 = 0 and x2 + y2 + 3x ...