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

##### Short Answer Type Questions related to Circle , S N Dey Mathematics | Class 11 | WBCHSE

30. A point moves in such a manner that the sum of the squares of its distance from the origin and the point is always Show that the locus of the moving point is a circle. Find the equation to the locus.

Solution.

Suppose that at any instant the co-ordinates of the moving point is

So, according to the problem,

Hence, by we get the locus of the point which is which represents the equation of a circle.

31. and are two given points and is a moving point ; if for all positions of , show that the locus of is a circle . Find the radius of the circle.

Solution.

Suppose that at any instant the the co-ordinates of the moving point is

Hence, by we get the locus of the point which is which represents the equation of a circle.

Comparing the circle with we get,

The radius of the circle is

32. Show that the locus of the point of intersection of the lines and when varies, is a straight line.

Solution.

Suppose that at any instant the point of intersection of two straight lines is

From and we get

So, by we get the locus of the point of intersection of the lines is

which represents the equation of a circle.

33. Whatever be the values of , prove that the locus of the point of intersection of the straight lines and is a circle. Find the equation of the circle.

Solution.

Suppose that at any instant the point of intersection of two straight lines is

and

Putting the value of in we get

Hence, by we get that the locus of the point of intersection of the straight lines is which represents the equation of a circle.

34. Show that, represent a circle passing through the origin. Find the co-ordinates of the centre and length of radius of the circle.

Solution.

Squaring both sides of and and adding , we get

Clearly, represents the equation of the circle with centre and radius unit.

35. Prove that the square of the distance between the two points and of the circle is

Solution.

Since the points and lies on the given circle, so

The square of the distance between the two points and of the circle is

36. The equations of two diameters of a circle are and and the length of the chord intercepted on the straight line by the circle is units. Find the equation of the circle.

Solution.

The centre of the circle is the intersection of and

Solving and , we get

So, the centre of the circle is

From the figure, we notice that

the distance of the given straight line from the point

From the figure, we notice that the the length of the chord intercepted on the straight line by the circle is so that

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

the equation of the circle

37. Find the equation of the circle circumscribing the rectangle whose sides are given by and

Solution.

From the figure, we notice that the point is the intersection of the straight lines

and

Now, solving and we get, the co-ordinates of

Again, from the figure, we notice that the point is the intersection of the straight lines and

So, solving and we get, the co-ordinates of

Clearly, represents the diameter of the circle.

Now, the equation of the diameter having extremities and is