M0IITU09 - Circles & system of circles qns

M0IITU09 - Circles & 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 : x 2 2 - 2 ax - 2 ay + a 2 = 0 x 2 2 + ax + ay = 0 x 2 2 + 2 ax + 2 by - a 2 None of these 3. The centres of the circles, x 2 2 = 1, x 2 + y 2 + 6x - 2y = 1 & x 2 + y 2 - 12x + 4y = 1 are : Same Collinear (C) Non - collinear (D) None of these 4. If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is (a, b) (b, a) a b 2 2 , b a 2 2 , - 5. The line l x + my + n = 0 will be a tangent to the circle, x 2 2 = a 2 if : n 2 ( l 2 + m 2 ) = a 2 a 2 ( l 2 2 ) = n 2 n ( l + m) = a 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 : 0 π 3 π 6 π 2 7. The locus of the middle points of those chords of the circle, x 2 2 = 4 which subtend a right angle at the origin is : x 2 + y 2 - 2x - 2y = 0 x 2 2 x 2 2 = 2 (x - 1) 2 + (y - 2) 2 = 5 8. A pair of tangents are drawn from the origin to the circle, x 2 2 + 20 (x + y) + 20 = 0 . The equation of the pair of tangents is : x 2 2 + 10 xy = 0 x 2 2 + 5 2 x 2 y 2 2 x 2 y 2 - 5 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 : (1 + m 2 ) ( (x 2 2 ) - 2 ax = 0 (1 2 ) (x 2 + y 2 ) - 2a (x + my) = 0 + m 2 2 + y 2 ) + 2a (x + my) = 0 (D) (1 + m 2 2 + y 2 ) - 2a (x - 10. If two circles, (x - 1) 2 + (y - 3) 2 = r 2 and x 2 2 - 8x + 2y + 8 = 0 intersect in two distinct points, then : 2 < r < 8 r = 2 r < 2 r > 2 11. touches both axes & whose centre is (x 1 , y 1 ) is : x 2 2 + 2x 1 (x + y) + x 1 2 x 2 2 - 2x 1 (x + y) + x 1 2 x 2 + y 2 = x 1 2 1 2 x 2 2 xx 1 yy 1 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 : (A) x 2 + y 2 + 2x - 2y = 62 (B) x 2 2 - 2x + 2y = 47 (C) x 2 2 + 2x - 2y = 47 (D) x 2 2 - 2x + 2y = 62 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 : 3 4 5 6 14. If the line l x + my = 1 be a tangent to the circle x 2 2 = a 2 , then the locus of the point ( l , m) is : A straight line A circle A parabola (D) None of these 15. The equation of a circle which touches both axes and the line, 3x - 4y + 8 = 0 and lies in the third quadrant is : x 2 + y 2 - 4x + 4y - 8 = 0 x 2 2 - 4x + 4y + 4 = 0 x 2 2 + 4x + 4y + 4 = 0 x 2 2 - 4x - 4y - 4 = 0 16. Tangents are drawn from the point (4, 3) to the circle x 2 2 = 9 . The area of the triangle formed by them and the line joining their points of contact is : 24 25 (B) 64 25 192 25 192 5 17. Circles x 2 2 - 2x - 4y = 0 and x 2 2 - 8y - 4 = 0 , Touch internally Touch externally Intersect each other at two distinct points Do not intersect each other at any point 18. The equations to the tangents to the circle, x 2 2 - 6x + 4y = 12 which are parallel to the straight line, 4x + 3y + 5 = 0, are : 3x - 4y - 19 = 0, 3x - + 31 = 0 4x + 3y - 19 = 0, 4x + + + + + - - + - + 19. The length of tangent from the point (5, 1) to the circle, x 2 2 + 6x - 4y - 3 = 0, is : 81 29 7 21 20. The length of common chord of the circle, (x - a) 2 2 2 x 2 + (y - b) 2 = b 2 2 a b 2 2 + a b a b 2 2 + 2 2 2 a b a b + None of these 21.
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This note was uploaded on 10/05/2011 for the course MATH 1201 taught by Professor Friesner during the Spring '11 term at St. Mary NE.

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

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