Intercept Made by Circle on Axes

Q. A circle touches x-axis and cuts off a constant length 2l from the y-axis. The locus of its centre is

1. + =
2. + = 2
3. + = 3
4. + =

Q. A line y =mx cuts the curve y square =4ax at point A and B. Find the equation of circle with AB as diameter

Q. find the equation of a circle which has the portion of the line 3x+4y=14 intercepted by the limnes x-y=0 and 11x-4y=0 as diameter

Q.

A circle passes through the origin O and cuts the axis at A(a, 0) and B(0, b). The reflection of O in the line AB is the point

1. $[\frac{2ab}{a^2+b^2},\frac{2ab}{a^2+b^2}]$
   

2. $[\frac{2a{b}^2}{a^2+b^2},\frac{2a^{2}b}{a^2+b^2}]$
   

3. $[\frac{2a^{2}b}{a^2+b^2},\frac{2a{b}^2}{a^2+b^2}]$
   

4. $(a,b)$
   

Q. 5. Find the equation of the circle whose centre is (3, -1) and which cut off an intercept of length 6 from the line 2x-5y+18=0

Q. A circle has radius 3 units and its centre lies on the line y=x-1. If it lasses through (7, 3), then its equation is

Q. The circle $x^2+y^2-3x-4y+2=0$ cuts x-axis at

1. (2, 0), (-3, 0)
2. (3, 0), (4, 0)
3. (1, 0), (-1, 0)
4. (1, 0), (2, 0)

Q. Consider a family of circles which are passing through the point (–1, 1) and are tangent to x-axis. (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

1. 
2. < k <
3. 
4. 

Q. 39. Equation of a circle whose centre is ( 3, - 1 ) and which cut off an intercept of length 6 units from the line 2x - 5y + 18 = 0 is _________

Q. lf the two circles $(x-1{)}^2+(y-3{)}^2=r^2$ and $x^2+y^2-8x+2y+8=0$ intersect in two distinct points then

1. $r<2$
2. $r>2$
3. $r=4$
4. $r=2$

Q.

The locus of the centre of a circle which touch the circles $x^2+y^2-6x-6y+14=0$ externally and also the Y - axis is given by

1. 

2. 

3. 

4. 

Q. A circle is circumscribed about a triangle with sides 20, 21 and 29, thus dividing the interior of the circle into 4 regions. Let A, B and C be the areas of the non triangular regions, with C being the largest. Then which one of the following holds True?

1. $A+B=C$
2. $A+B+210=C$
3. $A^2+B^2=C^2$
   
4. $20A+21B=29C$