Question
The two points A and B in a plane are such that for all points P lies on circle satisfied 
, then k will not be equal to
- 0
- 1
- 2
- None of these
The correct answer is: 1
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 the two points A and B in a plane are such that for all points P lies on circle satisfied .
Consider the circle as: x2+y2=1.
Now lets assume the points to be A(1,0), B(0,1), P(cosθ, sinθ).
Now we get:
Here we have given the two points A and B in a plane are such that for all points P lies on circle satisfied, so first we will get the equation of circle. Then we will find value of k with assumptions of trigonometric functions and then will find the final answer.
So here we have given the two points A and B in a plane are such that for all points P lies on circle satisfied . We can also use equation of circle to find the answer. So here the correct option is none of these.
Related Questions to study
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
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.
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
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.
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
For such questions, we have to see how the cricles are with respect to each other to find the distance between the centers.
touches the x-axis.
touches the x-axis if 
When a>0 and 
has complex roots.
cuts x-axis.
, the distance between the foci is
, 
, 
and 
, then 
equals
