Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

Circle \( \Large x^{2}+y^{2}-2x-nx-1=0 \) passes through two fixed points, co-ordinates of the points are

A) \( \Large \left(0,\ \pm 1\right) \)
B) \( \Large \left(\pm\ 1,\ 0\right) \)
C) \( \Large \left(0,\ 1\right)\ and\ \left(0,\ 2\right) \)
D) \( \Large \left(0,\ -1\right)\ and\ \left(0,\ -2\right) \)

Correct Answer:

A) \( \Large \left(0,\ \pm 1\right) \)

Description for Correct answer:
\( \Large \left(x^{2}+y^{2}-2x-1\right)+nx=0 \), they pass through intersection points of line x = 0 and circle.

\( \Large x^{2}+y^{2}-2x-1=0 \)

=> \( \Large y = \pm 1 \)

Therefore, Required points are \( \Large \left(0,\ \pm 1\right) \)

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

Comments

Similar Questions

1). Centre of circle whose normals are \( \Large x^{2}-2xy-3x+6y=0 \) is

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

B). \( \Large \left(3,\ -\frac{3}{2}\right) \)

C). \( \Large \left(\frac{3}{2},\ 3\right) \)

D). none of these

2). 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

3). 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

4). 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

5). 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

6). 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

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

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

9). 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

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