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The locus of centre of a circle \( \Large x^{2}+y^{2}-2x-2y+1=0 \) which rolls outside the circle \( \Large x^{2}+y^{2}-6x+8y=0 \) is:

A) \( \Large x^{2}+y^{2}-2x-2y-34=0 \)
B) \( \Large x^{2}+y^{2}-6x+8y+11=0 \)
C) \( \Large x^{2}+y^{2}-6x+8y-11=0 \)
D) none of these

Correct Answer:



C) \( \Large x^{2}+y^{2}-6x+8y-11=0 \)

Description for Correct answer:
Centre of required circle = \( \Large \left(3,\ -4\right) \)

Radius of Required circle = 5 + 1 = 6

Locus of circle is

\( \Large \left(x-3\right)^{2}+ \left(y+4\right)^{2} = 36 \)

=> \( \Large x^{2}-6x+9+y^{2}+16+8y = 36 \)

=> \( \Large x^{2}+y^{2}-6x+8y-11=0 \)

Part of solved Circles questions and answers : >> Elementary Mathematics >> Circles

Comments

Similar Questions

1). A line through \( \Large P \left(1,\ 4\right) \) intersect a circle \( \Large x^{2}+y^{2}=16 \) at A and B, then PA-PB is equal to:

A). 1

B). 2

C). 3

D). 4

2). AB, is a diameter of a circle and c is any point on circumference of the circle then:

A). the arc of \( \Large \triangle ABC \) is maximum, when it is isosceles

B). the area of \( \Large \triangle ABC \) is maximum, when it is isosceles

C). the perimeter of \( \Large \triangle ABC \) is maximum, when it is isosceles

D). none of the above

3). The number of common tangents to the circles \( \Large x^{2}+y^{2}-2x-4y+1=0 \) and \( \Large x^{2}+y^{2}-12x-16y+91=0 \) is

A). 1

B). 2

C). 3

D). 4

4). A, B, C and D are the points of intersection with the co-ordinate axes of the lines \( \Large ax+by=ab\ and\ bx+ay=ab \) then:

A). A, B, C, D are concyclic

B). A, B, C, D form a parallelogram

C). A, B, C, D form a rhombus

D). none of the above

5). The gradient of the radical axis of the circles \( \Large x^{2}+y^{2}-3x-4y+5=0\ and\ 3x^{2}+3y^{2}-7x+8y+11=0 \) is

A). \( \Large \frac{1}{3} \)

B). \( \Large -\frac{1}{10} \)

C). \( \Large -\frac{1}{2} \)

D). \( \Large -\frac{2}{3} \)

6). The limiting point of the system of circles represented by the equation \( \Large 2\left(x^{2}+y^{2}\right)+nx+\frac{9}{2}=0 \) are

A). \( \Large \left(\pm \frac{3}{2},\ 0\right) \)

B). \( \Large \left(0,\ 0\right)\ and\ \left(\frac{9}{2},\ 0\right) \)

C). \( \Large \left(\pm \frac{9}{2},\ 0\right) \)

D). \( \Large \left(\pm 3,\ 0\right) \)

7). The radical centre of the circles \( \Large x^{2}+y^{2}-16x+60=0,\) \( \Large x^{2}+y^{2}-12x+27=0,\) \( \Large x^{2}+y^{2}-12y+8=0 \) is

A). \( \Large \left(13,\ \frac{33}{4}\right) \)

B). \( \Large \left(\frac{33}{4},\ -13\right) \)

C). \( \Large \left(\frac{33}{4},\ 13\right) \)

D). none of these

8). The circles \( \Large x^{2} + y^{2} - 10x +16 = 0 \) and \( \Large x^{2} + y^{2} = r^{2} \) intersect each other at two distinct points if:

A). r < 2

B). r > 8

C). 2 < r < 8

D). \( \Large 2 \le r \le 8 \)

9). The centres of a set of circles, each of radius 3, lies on the circle \( \Large x^{2} + y^{2} = 25 \). The locus of any point in the set is:

A). \( \Large 4 \le x^{2}+y^{2} \le 64 \)

B). \( \Large x^{2}+y^{2} \le 25 \)

C). \( \Large x^{2}+y^{2}\ge 25 \)

D). \( \Large 3 \le x^{2}+y^{2} \le 9 \)

10). A variable circle passes through the fixed point A(p, q) and touches x-axis. The locus of the other end of the diameter through A is:

A). \( \Large \left(x-p\right)^{2}=4qy \)

B). \( \Large \left(x-q\right)^{2}=4py \)

C). \( \Large \left(y-p\right)^{2}=4qx \)

D). \( \Large \left(y-q\right)^{2}=4py \)