Intermediate maths-B Circle Imp 2 Marks problems

Circle 2 Marks IMP Problems

1)If the length of the tangent from (2,5) to the circle `x^2+y^2-5x+4y+k=0` is `sqrt(37)`,then find 'k'?

2)If the centre of the circle `x^2+y^2+ax+by-12=0` is (2,3) find the values of a,b and the radius of the circle?

3)If `x^2+y^2-4x+6y+c=0` represent a circle with radius 6 then find the vaue of c?

4)Find the values of a,b if `ax^2+bxy+3y^2-5x+2y-3=0` represents a circle.Also find radius and centre of the circle?

5) Find the other end of the diamter of the circle `x^2+y^2-8x-8y+27=0` if one end of it is (2,3)

6) Find the equation of the circle passing through (2,-1) and having the centre at (2,3)

7) find the equation of the circle passing through (3,4) and having the centre(-3,4)

8)Obtain the parametric equations of the circle `x^2+y^2-6x+4y-12=0`

9)Obtain the parametric equation of the circle `(x-3)^2+(y-4)^2=8^2`

10) Obtain the parametric equation of the circle `x^2+y^2=4`

11) Find the equation of the circle whose centre is (-4,3) and which passes through the origin.

12)Find the value of k if the points (4,k),(2,3) are conjugate with respect to the circle `x^2+y^2=17`

13) Find the power of the point (2,4) with respect to the circle `x^2+y^2-4x-6y-12=0`

14) Find the value of k if the points (4,2) and (k,-3) are conjugate with respect to the circle `x^2+y^2-5x+8y+6=0`

15) Find the Polar of (1,2) with respect to `x^2+y^2=7`

16)Find the pole of ax+by+c=0 (a≠0) with respect to `x^2+y^2=r^2`

17) If`x^2+y^2+2gx+2fy-12=0` represents a circle with centre (2,3) find g,f and its radius?

18)Find the value of 'a' if `2x^2+ay^2-3x+2y-1=0` represents a circle and also find its radius.

19) Find the equation of the circle whose extremities of a diameter are (-4,3) and (3,-4)

20) If the length of the tangent from 54 to the circle `x^2+y^2+2ky=0` is 1,then find k

21) Find the length of the tangent from (2,5) to the circle `x^2+y^2-25=0`

22) Find the equation of the polar of (1,2) with respect to the circle `x^2+y^2-10x-10y+25=0`

23) Find the value of k if the points (1,3) and (2,K) are conjugate with respect to the circle `x^2+y^2=35`

24) Find the power of point P(-1,1) with respect to the circle `x^2+y^2-6x+4y-12=0`

25) Find the centre and radius of the circle `sqrt(1+m^2)(x^2+y^2)-2cx-2mcy=0`

26)Find the equation of the circle which is concentric with `x^2+y^2-6x-4y-12=0` and passing through (-2,14)

27)If the circle `x^2+y^2-4x+6y+a=0` has radius 4 then find 'a'

28) Find the length of the chord formed by `x^2+y^2=a^2` on the line xcosα+ysinα=p

29)Find the chord of contact of (2,5) with respect to the circle `x^2+y^2-5x+4y-2=0`