Tiêu đề CIRCLES AND SYSTEM OF CIRCLES_DPP_questions_2025-06-04.pdf ✅

6. Equation of a circle touching the curve is (1) (2) (3) (4) 7. The centres of the circles , and are (1) Same (2) Collinear (3) Non-collinear (4) None of these 8. If the equation represents a circle, then (1) (2) (3) (4) 9. The equation of the circle whose diameters have the end points is given by (1) (2) (3) (4) 10. The equation of the circle passing through the origin and cutting intercepts of length and units from the positive axes, is (1) (2) (3) (4) DPP for LOCUS RELATED PROBLEM MATH Chapter: CIRCLES AND SYSTEM OF CIRCLES Topic: LOCUS RELATED PROBLEM Date: 04 Jun 2025 Type: DPP 1. Locus of the centre of circles which pass through and touches the line is - (1) (2) (3) (4) 2. Let be a variable point which moves in plane such that , where and . If and denote respectively the maximum and minimum value of , then value of is- (where [.] denotes the greatest integer function) (1) (2) (3) (4) 3. The locus of a point, which moves such that the sum of squares of its distances from the points is units, is a circle of diameter . Then is equal to ...... . (1) (2) (3) (4) |x − 1| + |y − 4| = 6 x 2 + y 2 − 2x − 8y − 18 = 0 x 2 + y 2 − 2x − 8y − 17 = 0 x 2 + y 2 − 2x − 8y + 1 = 0 x 2 + y 2 − 2x − 8y − 1 = 0 x 2 + y 2 = 1 x 2 + y 2 + 6x − 2y = 1 x 2 + y 2 − 12x + 4y = 1 K(x+1) 2 3 + (y+2) 2 4 = 1 K = 3 4 1 4 3 12 (a, 0),(0, b) x 2 + y 2 − ax − by = 0 x 2 + y 2 + ax − by = 0 x 2 + y 2 − ax + by = 0 x 2 + y 2 + ax + by = 0 3 4 x 2 + y 2 + 6x + 8y + 1 = 0 x 2 + y 2 − 6x − 8y = 0 x 2 + y 2 + 3x + 4y = 0 x 2 + y 2 − 3x − 4y = 0 (0, 1) y = x (x + y) 2 = 4y − 2 (x − y) 2 = 4y − 2 (x + y) 2 = 4x − 2 (x − y) 2 = 4x − 2 P(α, β) x − y PA PB = 2 A(1, 0) B(0, −1) M m α + β [ M m ] −1 −3 0 1 (0, 0),(1, 0),(0, 1)(1, 1) 18 d d 2 16 4 216 6
4. Let the locus of the mid points of the chords of circle drawn from the origin in- tersect the line at and . Then, the length of is : (1) (2) (3) (4) 5. A chord drawn from the point on circle meets to in such a way that , then the locus of point will be (1) Straight line (2) Circle (3) Parabola (4) None of these 6. From the origin, chords are drawn to the circle . The locus of mid points of these chords is a (1) Circle (2) Straight line (3) Pair of straight line (4) None of these 7. If a circle of constant radius passes through the origin and meets co-ordinate axes at and then the locus of the centroid of the triangle is (1) (2) (3) (4) 8. Let be the diameter of a semicircle . The locus of the centres of circles which are tangent to and to is an arc of (1) a circle (2) an ellipse (3) a parabola (4) a cycloid 9. A variable circle passes through the fixed point and touches the -axis . Then the locus of its centre is (1) A circle (2) An Ellipse (3) A hyperbola (4) A parabola 10. Let be a chord of the circle subtending a right angle at the centre. Then the lo- cus of the centroid of the as moves on the circle is (1) A parabola (2) A circle (3) An ellipse (4) A pair of straight lines DPP for TANGENT AND NORMAL TO A CIRCLE MATH Chapter: CIRCLES AND SYSTEM OF CIRCLES Topic: TANGENT AND NORMAL TO A CIRCLE Date: 04 Jun 2025 Type: DPP 1. The centre of the circle passing through the point and touching the parabola at the point is (1) (2) (3) (4) x 2 + (y − 1) 2 = 1 x + y = 1 P Q PQ 1 √2 √2 1 2 1 AB A(0, 3) x 2 + 4x + (y − 3) 2 = 0 M AM = 2AB M (x − 1) 2 + y 2 = 1 3k ′O′ A B OAB x 2 + y 2 = (2k) 2 x 2 + y 2 = (3k) 2 x 2 + y 2 = (4k) 2 x 2 + y 2 = (6k) 2 AB S AB S (2, 0) y AB x 2 + y 2 = r 2 ΔPAB P (0, 1) y = x 2 (2, 4) ( 3 10 , 16 5 ) ( −16 5 , 53 10 ) ( 6 5 , 53 10 ) ( −53 10 , 16 5 )