In the previous article , we discussed Very Short Answer Type Questions. In this article, we will discuss 10 more Short Answer type Questions from Chhaya Mathematics , Class 11 (S N De book ).

##### Short Answer Type Questions of Circle, S N Dey Mathematics, Class 11

11. The extremities of a diameter of a circle are the points and ; Find the equation of the circle. Also find the equation of that diameter of this circle which passes through the origin.

Solution.

The equation of any circle having the extremities and of a diameter is given by

Now, we need to find the equation of that diameter of this circle which passes through the origin.

The centre of the circle is

Hence equation of the diameter that passes through and is given by :

12. Find the equation of the circle through the points and and having its centre on the line

Solution.

Let be the centre of the circle.

Since lies on the line

Again, since the circle passes through the points and , the distance of from the points and , will be same.

Now, solving and we get,

So, the centre of the circle is and the radius of the circle is

Hence, the equation of the circle is

13. A circle has its centre on the straight line and cuts off the axis at the two points whose abscissae and find the equation of the circle and its radius.

Solution.

The general form of the equation of the circle can be written as

where is the centre of the circle and the radius

According to the problem, the circle passes through the points and

So, by we get

Similarly, by we get

Subtracting from we get,

Since the circle has its centre on the straight line , so

Putting the value of in we get

Now, putting the value of in we get

By we get the radius

By we get the equation of the circle as

14. The equation of a diameter of a circle is and it passes through the points and Find the equation of the circle , the co-ordinates of its centre and length of its radius.

Solution.

Let be the centre of the circle so that as the diameter of the circle passes through the centre of the circle.

Again, the circle passes through the points and so the centre is equidistant from the points and

Solving we get,

So, the centre of the circle is and radius of the circle is

the equation of the circle

15. A circle passes through through the points and its radius is unit ; find the equation of the circle.

Solution.

Let the centre of the circle be

the equation of the circle can be written as

which passes through the points and

Now, subtracting from we get,

By using we get,

So, the required equation of the circle is

and

or,

and are two diameters to the circle which passes through the point . Find its equation. Also find the radius of the circle.

Solution.

Clearly, the centre of the circle will be the intersection of two given diameters.

and are two given diameters.

Solving we get,

So, the centre of the circle is : Also, it is given that the circle passes through the point .

Hence, the radius

Finally, the equation of the circle is

17. A circle passes through the points and its centre lies on the axis. Find the equation of the circle.

Solution.

Let the centre of the circle because the centre lies on the axis. Since the circle passes through the points , the points are equidistant from the centre of the circle.

the centre of the circle

the radius of the circle

the equation of the circle is

18. Find the equation of the circle which has its centre on the line and which passes through the points and

Solution.

Let the centre of the circle be as its centre lie on the line

Since the circle passes through the points , the points are equidistant from the centre of the circle.

the centre of the circle and radius

the equation of the circle is

19. Find the equation to the circle which touches the axis at the origin and passes through the point

Solution.

Since the circle which touches the axis at the origin, from the following figure we notice that the centre of the circle lies on the axis.

Let the radius of the circle and the co-ordinate of the centre of the circle Now, since the circle passes through the point the radius of the circle is the distance between and

Now, the equation of the circle with centre and radius is

20. A circle touches the axis at and its radius is twice the radius of the circle find the equation of the circle and the length of its chord intercepted on the axis.

Solution.

We can rearrange the given circle as

So, the radius of the circle as represented by is unit. Our circle of concern will have a radius of units. Now, suppose that the centre of circle of concern is so that the equation of circle can be written as

Now, the circle in passes through so that

the equation of the circle

Comparing with the general form of the equation of circle we get,

So, the length of the chord cut on axis