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 `