Revision Quiz on Circle for JEE & BITSAT Exams

Question 1

Let ABCD be a trapezium with parallel sides AB and CD such that the circle S with AB as its diameter touches CD. Further, the circle S passes through the midpoints of the diagonals AC and BD of the trapezium. The smallest angle of the trapezium is

Question 2

The circle x² + y² = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if

Question 3

Centre and radius of the circle with segment of the line x + y = 1 cut off by coordinate
axes as diameter is

Question 4

If P and Q are the points of intersection of the circles x² +y²+3x+7y+2p-5 =0 and x²+y² +2x +2y- p² =0, then there is a circle passing through P, Q and (1, 1) for

Question 5

The lines 2x-3y=5 and 3x-4y=7 are diameters of a circle of area 154sq. units. Then equation of circle is

Question 6

Equation of circles touching x-axis at the origin and the line 4x – 8y + 15 = 0 are

Question 7

If a circle C, whose radius is 3, touches externally the circle, x²+y²+2x-4y-4=0 at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to

Question 8

Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices(

are touching the circle

are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d is

Question 9

If the common tangents to the parabola, x²=4y and the circle, x²+y²=4 intersect at the point P, then the distance of P from the origin, is:

Question 10

If one of the diameters of the circle, given by the equation, x² + y² – 4x + 6y – 12 = 0, is a chord of a circle S, whose centre is at (–3, 2), then the radius of S is:

Question 11

If the circles x² + y² + 2gx + 2fy + c = 0 bisects the circumference of the circle x² + y²+ 2g ' x + 2 f ' y + c' = 0 then the length of the common chord of these two circles is -

Question 12

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 and 5x² + 5y² – 48x + 64y + 300 = 0 are in the ratio

Question 13

Equation of a circle that cuts the circle

and lines x = – g and y = –f orthogonally, is;

Question 14

The angle between a pair of tangents drawn from a point P to the circle x² + y² + 4x-6y+9sin²φ+13cos² φ = 0 is 2. The equation of the locus of the point P is

Question 15

Let

and let

, be circles with radii

, respectively. Assume that

and

touch externally for

. It is also given that the

-axis and the line

are tangential to each of the circles. Then

are in