A to Z Exams

The angle between the tangents drawn from (0,0) to the circle x2+y2+4x-6y+4=0 is

The length of the tangent from the point (-1, 1) to the circle x2+y2-4x+k=0 is equal to 2 then k=

The lengths of the tangents from any point on the circle 15x2+15y2-48x+64y=0 to the two circles 5x2+5y2-24x+32y+75=0, 5x2+5y2-48x+64y+300=0 are in the ratio

If the two circles (x-2)2+(y-3)2=r2and x2+y2-10x+2y+17=0 intersect in two distrinct points then

How many circles can be drawn each touching all the three lines x+y=1, x+1=y, 7x-y=6

If x2+y2+6x+2ky+25=0 touches the y-axis then k=

The equation of the circle having centre on the line x+y=1 and touching the lines 3x-4y+2=0, 4x+3y+7= 0 is

The area of the triangle formed by the tangents from (1, 3) to the circle x2+y2-4x+6y+1=0 and its chord of contact is

If the length of the tangets from two points A, B to a circles are 6, 7 respectively. If A, B are conjugate points then AB=

Let A be the centre of the circle x2+y2-2x-4y-20=0. Suppose that the tangent at the point B(1, 7) and D(4, -2) on the circle meet at the point C. The area of the quadrilateral ABCD is

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

If the polars of points on the circle x2+y2= a2 w.r.t the circle x2+y2= b2  touch the circle x2+y2= c2, then a, b, c are in

The area of the quadrilateral formed by the tangents from the point (4,5) to the circle x2+y2-4x-2y-11=0 with a pair of radii joining the points of contact of these tangents is

The parametric equations of circle (x-3)2+(y-2)2=100 are

The circle orthogonal to the  three circles x2+y2+aix+biy+c=0, i=1, 2, 3 is

The length of the intercept made by the circle x2+y2-12x+14y+11=0 on x-axis is

The circle x2+y2=4 cuts the circle x2+y2-2x-4=0 at the points A and B. If the circle x2+y2-4x-k=0 passes through A and B then the value of k is

The nearest point on the circle x2+y2-6x-4y-12=0 from (-5, 4) is

The equation of the circle with centre at (-3, 4) and touching y-axis is

The centre of the incircle of the triangle formed by the line 3x+4y=24 with the axes is

If the circles x2+y2=3a2 , x2+y2-6x-8y+9=0 touch externally then a=

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is

If the length of the tangent from (h, k) to the circle x2+y2=16 is twice the length of the tangent from the same point to the circle x2+y2+2x+2y=0, then

The equation of the common tangent at the point contact of the circles x2+y2-10x+2y+10=0, x2+y2-4x-6y+12=0 is

For the circles x2+y2+4x+2y-4=0, x2+y2-4x-2y+4=0 the line 3x+4y-5=0 is a

The equation of the circle with centre (-1, 1) and touching the circle x2+y2-4x+6y-3=0 externally is

The equations of the tangents to the circle x2+y2=16 which are inclined at an angle of 600 to the x-axis is

For the circle x2+y2-2x-4y-4=0 the lines 2x+3y-1=0, 2x+y+5=0 are

The longest distance from (-3, 2) to the circles x2+y2-2x+2y+1=0 is

Let A and B be any two points on each of the circles x2+y2-8x-8y+28=0 and x2+y2-2x-3=0 respectively. If d is the distance between A and B then the set of all possible values of d is