Topics
If \( \Large 5x-12y=10 \) and \( \Large 12y-5x+16=0 \) are two tangents to a circle, then the radius of the circle is
|
A) 1 |
|
B) 2 |
|
C) 4 |
|
D) 6 |
Correct Answer:
| A) 1 |
Description for Correct answer:
Given tangents are \( \Large 5x-12y+10=0, \)
and \( \Large 5x-12y-16=0 \) parallel.
Radius = \( \Large \frac{c_{1} - c_{2}}{2\sqrt{a^{2} + b^{2}}} \)
Radius = \( \Large \frac{c_{1}-c_{2}}{2\sqrt{5^{2}+ \left(-12\right)^{2} }} = \frac{26}{2 \times 13} = 1 \)
Part of solved Circles questions and answers : >> Elementary Mathematics >> Circles
Comments
Similar Questions
1). Equation of the circle passing through the point \( \Large \left(3,\ 4\right) \) and concentric with the circle \( \Large x^{2}+y^{2}-2x-4y+1=0 \) is
| ||||
2). Circle \( \Large x^{2}+y^{2}-2x-nx-1=0 \) passes through two fixed points, co-ordinates of the points are
| ||||
3). Centre of circle whose normals are \( \Large x^{2}-2xy-3x+6y=0 \) is
| ||||
4). 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:
| ||||
5). 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:
| ||||
6). AB, is a diameter of a circle and c is any point on circumference of the circle then:
| ||||
7). 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
| ||||
8). 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:
| ||||
9). 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
| ||||
10). 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
|
