class11 maths ch11 circle extra question

Ncert
Class11 maths ch11 
Extra Question

Find the equation of a circle with centre the centres of the circles . (a, 0) and radius a. 

(a) x+y+ 2ax = 0 (6) x*+ y - 2ax = 0 

(c)x+ + 2ay = 0 

Find the equation of the circle which passes

through the point (4, 5) and has its centre at 

(2, 2).

(a) (x+ 2)+(y + 2) = 13 

(b) (x - 3) + (y - 2) = 13 

(x-2) +(y - 4)} -65 and 

(x-4) +(y- 6) = 64 (d) x+ y - 2ay = 0 

12. Find the equation of the circle which passes

through origin and cuts off intercepts -2 and 

3 on x-axis and y-axis respectively. 

13. Find the equation of the circle whose 

radius is 5 and which touches the circle

(c) (x-2)+ (y- 2)* = 13 x+-2x -4y 20 = 0 externally at the 

(d) (x- 2) +(y - 3)* =13 point (3, 7). 

. Find the centre of the circle x + y+2y = 0. 

(a) (0, -1) 

(c) (0, 1) 

14. Show that the equation of the circle which 

touches the coordinates axis and whose (b) (-1,0)

(d) (1,0)

4. The area of the circle centred at (1, 2) and 

passing through (4, 6) is 

(a) 57t 

centre lies on the line lx + my +n = 0 is 

+m)(x* +)+ 2n ( + m) (x +y) +* = 0 

15. Find the area of an equilateral triangle

(b) 107t inscribed in the circlex ++2gx +2fy+c=0. 

(c) 257t (d) None of these (NCERT)

5. Write the equation of circle with centre 16. Find the equation of circle with radius 

5 whose centre lies on x-axis and passes 

through the point (2, 3). 

(-a, -b) and radius a +b. (KVS 2014)

(NCERT) 6. Find the equation of circle whose centre is 

(-1,2) and radius is 4. 17. Find the equation of a circle of radius 

5 units which is touching another circde 

x+y - 2x - 4y - 20 =0 at the point (5, 5). 

(NCERT Exemplar) 

(KVS 2017) 

SA (2 marks)

If the lines 3x - 4y + 4 = 0 and 6x -8y- 7 0 

are tangents to a circle, then find the radius of 

the circle.

18. Find the equation of the circle passing 

through (0, 0) and making intereepts a andb (NCERT Exemplar) 

on the coordinate axes. Find the equation of a circle which touches

both the axes and the line 3x - 4y +8 = 0 and 

lies in the third quadrant. (NCERT Exemplar) 

If one end of a diameter of the circle x* + 

-4x 6y + 11 = 0 is (3, 4), then find the 

cOordinate of the other end of the diameter. 

(NCERT, NCT 2012. 2013) 

19. Find the equation ot the circle which is 

circumscribed about the triangle whose 

vertices are (-2, 3). (5, 2) and (6, -1). 

(NCT 2016) 

(NCERT Exemplar) 20. Find the equation ot the circle passing 

through (0, 0) and making intercepts 5 and7 LAT (KVS 2017) (4 marks) on coordinate axes. 

Fnd the equation of a circle whose centre is 

,-2) and which passes through the centre 

of the circle r+ y - 4x - 6y + 11 = 0. 

21. Find the equation of circle which passes 

through the points (2, -2), (3, 4) and has its 

centre on the line 2x +2y= 7. (2019)