Circle and a Point

IMPORTANT

Circle and a Point: Overview

This topic covers concepts such as Interaction between Point and a Circle, Position of a Point with Respect To a Circle, Distance of a Point from a Circle, Greatest Distance of a Point from a Circle, Least Distance of a Point from a Circle, etc.

Important Questions on Circle and a Point

MEDIUM
IMPORTANT

1,22 is a point on circle x2+y2=9. Which of the following is a point on the circle at 2 units distance from 1,22?

MEDIUM
IMPORTANT

The maximum distance of any point on the circle x-72+y-2302=16 from the Centre of the ellipse 25x2+16y2=400 is 

EASY
IMPORTANT

The equation of the radical axis of the circles x2+y2+4x+6y-7=0 and 4x2+y2+8x+12y-9=0 is

MEDIUM
IMPORTANT

If the points 1,3 and (2,k) are conjugated with respect the circle x2+y2=35, then the value of k is

MEDIUM
IMPORTANT

If the point 1,4 lies inside the circle x2+y2-6x-10y+p=0 and the circle does not touch or intersect the coordinates axes, then

HARD
IMPORTANT

From the point A0,3 on the circle x2+9x+y-32=0, a chord AB is drawn and extended to a point M, such that AM=2AB ( B lies between A & M). Then, the locus of the point M is

HARD
IMPORTANT

If M and m are the maximum and minimum values of yx for pair of real numbers x,y which satisfy the equation x-32+y-32=6, then the value of 1M+1m is

EASY
IMPORTANT

The value of a such that the power of the point 1, 6 with respect to the circle x2+y2+4x-6y-a=0 is -16 is

HARD
IMPORTANT

The sum of the minimum and maximum distances of the point (4, -3) to the circle x2+y2+4x-10y-7=0 is

HARD
IMPORTANT

The sum of the minimum and maximum distances of the point (4, -3) to the circle x2+y2+4x-10y-7=0 is

MEDIUM
IMPORTANT

Difference between maximum & minimum distance of point (2, -7) from x2+y2-14x-10y-151=0 is

MEDIUM
IMPORTANT

Let A(1, 2), B(3, 4) be two points and C(x, y) be a point such that (x  1) (x  3) + (y  2) (y  4) = 0 . If area of ABC is 1 sq. unit. Then maximum number of positions of C in xy plane is

EASY
IMPORTANT

Maximum distance of any point on the circle  x -72+ y -2 302=16 from the centre of the ellipse 25x2+ 16y2=400 is

MEDIUM
IMPORTANT

If the point 2,k lies outside the circles x2+y2+x-2y-14=0 & x2+y2=13, then

MEDIUM
IMPORTANT

A3,1,B6,5 and Cx,y are three points such that angle ACB is a right angle and the area of triangle ABC=7sq.unit , then the number of such point C is

EASY
IMPORTANT

The radius of the circle passing through the point 6,2 and two of whose diameters are x+y=6 and x+2y=4 is -

HARD
IMPORTANT

If the point 2, k lies outside the circles x2+y2=13 and x2+y2+x-2y-14=0, then

HARD
IMPORTANT

Difference between maximum & minimum distance of point 2,  7 from x2+y214x10y151=0 is

HARD
IMPORTANT

If P and Q are two points on the circle x2+y2-4x- 4y-1=0 which are farthest and nearest respectively from the point 6, 5 , then -

HARD
IMPORTANT

If θ is the angle subtended by the circle S=x2+y2+2gx+2fy+ c=0  at the point Px1, y1 and S1=x12+y12+2gx1+2fy1+c, then