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M0IITU09 - Circles &amp; system of circles qns

M0IITU09 - Circles &amp; system of circles qns -...

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1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. If the line x + 2 by + 7 = 0, is a diameter of the circle, x 2 + y 2 - 6x + 2y = 0 then b = (A) 3 (B) - 5 (C) - 1 (D) 5 2. The equation of the circle which touches both the axes & whose radius is a, is : 3. The centres of the circles, x 2 + y 2 = 1, x 2 + y 2 + 6x - 2y = 1 & x 2 + y 2 - 12x + 4y = 1 are : 4. If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is 5. The line l x + my + n = 0 will be a tangent to the circle, x 2 + y 2 = a 2 if : (A) n 2 ( l 2 + m 2 ) = a 2 (B) a 2 ( l 2 + m 2 ) = n 2 (C) n ( l + m) = a (D) a ( l + m) = n 6. The angle between the two tangents from the origin to the circle, (x - 7) 2 + (y + 1) 2 = 25 is : (A) 0 (B) π 3 (C) π 6 (D) π 2 7. The locus of the middle points of those chords of the circle, x 2 + y 2 = 4 which subtend a right angle at the origin is : 8. A pair of tangents are drawn from the origin to the circle, x 2 + y 2 + 20 (x + y) + 20 = 0 . The equation of the pair of tangents is : 9. y = mx is a chord of a circle of radius a and the diameter of the circle lies along x-axis and one end of the chord is origin . The equation of the circle described on this chord as diameter is : 10. If two circles, (x - 1) 2 + (y - 3) 2 = r 2 and x 2 + y 2 - 8x + 2y + 8 = 0 intersect in two distinct points, then : (A) 2 < r < 8 (B) r = 2 (C) r < 2 (D) r > 2 11. The equation of the circle which touches both axes & whose centre is (x 1 , y 1 ) is : 2 = 0 2 = 0 2 + y 1 2 Circles & System of Circles

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2 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 12. The lines, 2x - 3y = 5 & 3x - 4y = 7 are the diameters of a circle of area 154 sq. units . The equation of the circle is : 13. A circle touches the y-axis at the point (0, 4) & cuts the x-axis in a chord of length 6 units . The radius of the circle is : 14. If the line l x + my = 1 be a tangent to the circle x 2 + y 2 = a 2 , then the locus of the point ( l , m) is : (A) A straight line (B) A circle (C) A parabola (D) None of these
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