Maths-
General
Easy

Question

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

## The correct answer is: A parabola

### The locus is the collection of all points that satisfy the requirements and create geometrical shapes like lines, line segments, circles, curves, etc. Only curved shapes are defined for the locus. Both regular and irregular shapes are possible.The circle's equation with its centre at (h, k) and radius 'a' is (x-h)2+(y-k)2 = a2 which is called the standard form for the equation of a circle.Now we have given a circle that touches the x-axis and also touches the circle with a centre at (0, 3) and radius, let the centre be (h,k). As the centre is touching the x-axis, then r1=k We have also given that circle touches with (0,3) and radius 2, so:Here we have given that a circle touches the x-axis and also touches the circle with centre at (0, 3) and radius, so first we will get the equation of a circle. Then we will find the locus by using the formula, and then the resulting locus will be answered.

So here we have given to find the locus is in which form. We used the concept of circles and solved the question. We can also use equation of circle to find the answer. So the locus is x2-10y+5=0, this is the representation of parabola, so correct answer is parabola.