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A circle touches the x -axis and also touches the circle with centre at (0,3) and radius 2. The locus of the centre of the circle is

Options

  1. Aan ellipse
  2. Ba circle
  3. Ca hyperbola
  4. Da parabola

Correct answer

D. a parabola

Step-by-step solution

Equation of circle with centre (0,3) and radius 2 is x^2+(y-3)^2=4 Let locus of the variable circle is ( , ) It touches x -axis. It equation (x- )^2+(y- )^2= ^2 Circles touch externally aligned & ^2+( -3)^2 =2+ & ^2+( -3)^2= ^2+4+4 & ^2=10( -1 / 2) aligned Locus is x^2=10(y-1 / 2) which is parabola.

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