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

2.

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

3.

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

4.

If two circle (x – 1)^{2} + (y – 3)^{2} = a^{2} and x^{2} + y^{2} – 8x + 2y + 8 = 0 intersect in two distinct points, then -

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

6.

Two tangents to the circle x2 + y2 = 4 at the points A and B meet at P(–4, 0). The area of the quadrilateral PAOB, where O is the origin is -

7.

The radius of the circle passing through the points (5, 2), (5, –2) and (1, 2) is

8.

y = mx + C touches the circle, if C2 = a2 (1 + m2) Now, ycos? = xsin? – k

y = xtan? – ksec? ? k2sec2? = k2 (1 + tan^{2}) True for all value of

9.

One of the diameters of the circle circumscribing the rectangle ABCD is x – 4y + 7 = 0. If A and B are points (–3, 4) and (5, 4) respectively, then the area of the rectangle is-

10.

Let C be the centre of the circle x2 + y2 – 2x – 4y – 20 = 0. If the tangents at the point A(1, 7)

and B(4, –2) on the circle meet at piont D. Then area of the quadrilateral ABCD is-