MCQ (Previous Year Questions) - Circles (Level 1) - JEE MCQ

If a circle passes through the point (a, b) and cuts the circle x² + y² = 4 orthogonally, then the locus of its centre is -              

[AIEEE-2004]

A variable circle passes through the fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is -              

[AIEEE-2004]

If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference 10p, then the equation of the circle is -                            

[AIEEE-2004]

If the circles x² + y² + 2ax + cy + a = 0 and x² + y² – 3ax + dy – 1 = 0 intersect in two distinct point P and Q then the lines 5x + by – a = 0 passes through P and Q for -      

[AIEEE-2005]

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 -          

[AIEEE-2005]

If a circle passes through the point (a, b) and cuts the circle x² + y² = p² orthogonally, then the equation of the locus of its centre is -                      

[AIEEE-2005]

If the pair of line ax² + 2(a + b)xy + by² = 0 lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then      

[AIEEE-2005]

If thel ines 3x – 4y – 7 = 0 and 2x – 3y – 5 = 0 are two diameters of a circle of area 49p square units, the equation of the circle is -                  

[AIEEE-2006]

Let C be the circle with centre (0,0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle c that subtend an angle of at its centre is -      

[AIEEE-2006]

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                   

 [AIEEE-2007] 

The point diametrically opposite to the point P(1, 0) on the circle x² + y² + 2x + 4y – 3 = 0 is -

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

[AIEEE-2010]

The two circles x² + y² = ax and x² + y² = c² (c > 0) touch each other if :      

[AIEEE-2011]

The length of the diameter of the circle which touches the x-axis at the pint (1, 0) and passes through the point (2, 3)        

[AIEEE-2012]

The circle passing through (1, –2) and touching the axis of x at (3, 0) also passes through the point :