Test Preparation on Mathematics-Circle and Conic Section

1.

The number of integral values of m for which x2 + y2 (1 – m)x + my + 5 = 0 is the equation of a circle whose radius cannot exceed 5, is

120
218
38
424

2.

The circle x² + y² – 6x – 10y + P = 0 does not touch or intersect the coordinate axes and point (1, 4) is inside the circle, then the range of the values of P is

1(0, 25)
2(5, 29]
3(25, 29)
4(9, 25)

3.

Equation of smallest circle touching these four circle (x +- 1)² + (y +- 1)² = 1 is

1x2 + y2 = 3 –√2
2x2 + y2 = 5 – 2 √2
3x2 + y2 =6 – 2 √2
4x2 + y2 = 3 – 2 √2

4.

If two circle (x – 1)² + (y – 3)² = a² and x² + y² – 8x + 2y + 8 = 0 intersect in two distinct points, then -

12 < a < 8
2a > 2
3a < 2
4a = 2

If d is the distance between the centre of two circles of radii r1 and r2, then they intersect
in two distinct points, iff | r1 – r2 | < d < r1 + r2
Here, radii of two circles are a and 3 and distance between the centre is 5.
Thus | a – 3 | < 5 < a + 3 ? –2 < a < 8 and a > 2
? 2 < a < 8

5.

If the tangents are drawn to the circle x2 + y2 = 12 at the point where it meets the circle x2 + y2 – 5x + 3y – 2 = 0, then the point of intersection of these tangent is

1a
2b
3c
4d


Right Ans	Wrong Ans	Not Attempted

The number of integral values of m for which x2 + y2 (1 – m)x + my + 5 = 0 is the equation of a circle whose radius cannot exceed 5, is

The circle x2 + y2 – 6x – 10y + P = 0 does not touch or intersect the coordinate axes and point (1, 4) is inside the circle, then the range of the values of P is

Equation of smallest circle touching these four circle (x +- 1)2 + (y +- 1)2 = 1 is

If two circle (x – 1)2 + (y – 3)2 = a2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then -

If the tangents are drawn to the circle x2 + y2 = 12 at the point where it meets the circle x2 + y2 – 5x + 3y – 2 = 0, then the point of intersection of these tangent is

Check your progress:

The circle x² + y² – 6x – 10y + P = 0 does not touch or intersect the coordinate axes and point (1, 4) is inside the circle, then the range of the values of P is

Equation of smallest circle touching these four circle (x +- 1)² + (y +- 1)² = 1 is

If two circle (x – 1)² + (y – 3)² = a² and x² + y² – 8x + 2y + 8 = 0 intersect in two distinct points, then -