Conic Sections Exercise 11.1
Exercise 11.1
In each of the following Exercises 1 to 5, find the equation of the circle with:
1. Centre (0, 2) and radius 2.
Ans. Given: 
and 
Equation of the circle = 
2. Centre 
and radius 4.
Ans. Given: 
and 
Equation of the circle =
3. Centre 
and radius 
Ans. Given: 
and 
Equation of the circle =
4. Centre 
and radius 
Ans. Given: 
and 
Equation of the circle:
5. Centre 
and radius 
Ans. Given: 
and 
Equation of the circle =
In each of the following Exercises 6 to 9, find the centre and radius of the circles.
6. 
Ans. Given: Equation of the circle:
……….(i)
On comparing eq. (i) with
and 
7. 
Ans. Given: Equation of the circle:
……….(i)
On comparing eq. (i) with
and 
8. 
Ans. Given: Equation of the circle: 
……….(i)
On comparing eq. (i) with
and 
9. 
Ans. Given: Equation of the circle:
……….(i)
On comparing eq. (i) with
and 
10. Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 
Ans. The equation of the circle is ……….(i)
Circle passes through point (4, 1)
……….(ii)
Again Circle passes through point (6, 5)
……….(iii)
From eq. (ii) and (iii), we have
……….(iv)
Since the centre 
of the circle lies on the line 
……….(v)
On solving eq. (iv) and (v), we have 
Putting the values of 
and 
in eq. (ii), we have
Therefore, the equation of the required circle is
11. Find the equation of the circle passing through the points (2, 3) and 
and whose centre is on the line 
Ans. The equation of the circle is ……….(i)
Circle passes through point (2, 3)
……….(ii)
Again Circle passes through point (–1, 1)
……….(iii)
From eq. (ii) and (iii), we have
……….(iv)
Since the centre of the circle lies on the line 
……….(v)
On solving eq. (iv) and (v), we have 
Putting the values of and in eq. (ii), we have
Therefore, the equation of the required circle is
12. Find the equation of the circle with radius 5 whose centre lies on 
axis and passes through the point (2, 3).
Ans. Since the centre of circle lies on axis, therefore the coordinates of centre is 
Now the circle passes through the point (2, 3). According to the question,
or 
Taking , Equation of the circle is 
Taking , Equation of the circle is 
13. Find the equation of the circle passing through (0, 0) and making intercept 
and 
on the coordinate axes.
Ans. The circle makes intercepts with axis and with 
axis.
OA = and OB =
Coordinates of A and B are 
and 
respectively.
Now the circle passes through the points O (0, 0), A and B.
Putting these coordinates of three points in the equation of the circle,
………(i)
And 
And 
Putting the values of 
and 
in eq. (i), we have
14. Find the equation of the circle with centre (2, 2) and passes through the point (4, 5).
Ans. The equation of the circle is ……….(i)
Since the circle passes through point (4, 5) and coordinates of centre are (2, 2).
Radius of circle = 
= 
= 
Therefore, the equation of the required circle is
15. Does the point 
lie inside, outside or on the circle 
?
Ans. Given: Equation of the circle
On comparing with , we have 
and 
Now distance of the point from the centre (0, 0)
= 
= 
= 
= 4.3 <5
Therefore, the point lies inside the circle.