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

- A hyperbola
- A parabola
- An ellipse
- A circle

## 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} = a^{2} 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 x^{2}-10y+5=0, this is the representation of parabola, so correct answer is parabola.^{ }

### Related Questions to study

Maths-

### If d is the distance between the centres of two circles, are their radii and , then

For such questions, we have to see how the cricles are with respect to each other to find the distance between the centers.

### If d is the distance between the centres of two circles, are their radii and , then

Maths-General

For such questions, we have to see how the cricles are with respect to each other to find the distance between the centers.

maths-

### Assertion (A): The curve touches the x-axis.

Reason(R): touches the x-axis if

### Assertion (A): The curve touches the x-axis.

Reason(R): touches the x-axis if

maths-General

maths-

### Assertion (A): When a>0 and has complex roots.

Reason(R): The graph of cuts x-axis.

### Assertion (A): When a>0 and has complex roots.

Reason(R): The graph of cuts x-axis.

maths-General

maths-

### In an ellipse , the distance between the foci is

### In an ellipse , the distance between the foci is

maths-General

maths-

### If , , and , then equals

### If , , and , then equals

maths-General

chemistry-

### Arrange the following in decreasing order of their solubility in water

### Arrange the following in decreasing order of their solubility in water

chemistry-General

chemistry-

### Which have maximum solubility in water, for nearly same molecular weight compounds

### Which have maximum solubility in water, for nearly same molecular weight compounds

chemistry-General

chemistry-

### The correct order of solubility in water is :

a) CH_{3}OH

b) CH_{3}CH_{2}OH

c)

d)

### The correct order of solubility in water is :

a) CH_{3}OH

b) CH_{3}CH_{2}OH

c)

d)

chemistry-General

chemistry-

### Decreasing order of melting point of compound I - IV follows :

### Decreasing order of melting point of compound I - IV follows :

chemistry-General

chemistry-

### Decreasing order of melting point of compound I to IV follows

### Decreasing order of melting point of compound I to IV follows

chemistry-General

chemistry-

### Which order is correct regarding melting point ?

### Which order is correct regarding melting point ?

chemistry-General

chemistry-

### Decreasing order of boiling point of I to IV follow

### Decreasing order of boiling point of I to IV follow

chemistry-General

chemistry-

### The correct boiling point order is :

### The correct boiling point order is :

chemistry-General

chemistry-

### Arrange the following in decreasing order of their boiling points

### Arrange the following in decreasing order of their boiling points

chemistry-General

chemistry-

### Decreasing order of boiling point of I - IV follows

### Decreasing order of boiling point of I - IV follows

chemistry-General