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 = 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.
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) CH3OH
b) CH3CH2OH
c) 
d) 
The correct order of solubility in water is :
a) CH3OH
b) CH3CH2OH
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
