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The Value of c for which the line \( \Large y=2x+c \) is a tangent to the circle \( \Large x^{2}+y^{2}=16 \) is:

A) \( \Large -16\sqrt{5} \)
B) \( \Large 4\sqrt{5} \)
C) \( \Large 16\sqrt{5} \)
D) 20

Correct Answer:


B) \( \Large 4\sqrt{5} \)

Description for Correct answer:

Given that \( \Large y = 2x+c \) ...(i)

\( \Large x^{2}+y^{2}=16 \) ...(ii)

We Know that, if \( \Large y = mx+c \) is tangent to the circle \( \Large x^{2}+y^{2}=a^{2} \) then \( \Large c = \pm a\sqrt{1+m^{2}} \) here m = 2, a = 4

\( \Large c = \pm 4\sqrt{1+2^{2}} = \pm 4\sqrt{5} \)

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

Comments

Similar Questions

1). The radical axis of two circle and line joining their centres are:

A). Parallel

B). Perpendicular

C). Neither Parallel nor perpendicular

D). Intersecting but not perpendicular

2). Which of the following is a point on the common chord of the circles \( \Large x^{2}+y^{2}+2x-3y+6=0\ and\ x^{2}+y^{2}+x-8y-13=0 \)?

A). \( \Large \left(1,\ -2 \right) \)

B). \( \Large \left(1,\ 4\right) \)

C). \( \Large 1,\ 2 \)

D). \( \Large \left(1,\ -4\right) \)

3). The radius of the circle passing through the point \( \Large \left(6,\ 2\right) \) and two of whose diameter are \( \Large x+y=6\ and\ x+2y=4 \) is:

A). 4

B). 6

C). 20

D). \( \Large \sqrt{20} \)

4). The radius of any circle touching the lines \( \Large 3x-4y+5=0\ and\ 6x-8y-9=0 \) is:

A). 1.9

B). 0.95

C). 2.9

D). 1.45

5). The locus of the middle point of the chords of the circle \( \Large x^{2}+y^{2}=a^{2} \) such that the chords pass through a given point \( \Large \left(x_{1},\ y_{1}\right) \) is:

A). \( \Large x^{2}+y^{2}-xx_{1}-yy_{1}=0 \)

B). \( \Large x^{2}+y^{2}=x^{2}_{1}+y^{2}_{1} \)

C). \( \Large x+y=x_{1}+y'_{2} \)

D). \( \Large x+y=x^{2}_{1}+y^{2}_{1} \)

6). The equations of the tangents to the circle \( \Large x^{2}+y^{2}-6x+4y-12=0 \) which are parallel to the line \( \Large 4x+3y+5=0 \),are

A). \( \Large 4x+3y+11=0 \) and \( \Large 4x+3y+8=0 \)

B). \( \Large 4x+3y-9=0 \) and \( \Large 4x+3y+7=0 \)

C). \( \Large 4x+3y+19=0 \) and \( \Large 4x+3y-31=0 \)

D). \( \Large 4x+3y-10=0 \) and \( \Large 4x+3y+12=0 \)

7). The lines \( \Large 2x-3y=5\ and\ 3x-4y=7 \) are diameters of a circle having area as 154 sq unit. Then the equation of the circle is:

A). \( \Large x^{2}+y^{2}+2x-2y=62 \)

B). \( \Large x^{2}+y^{2}+2x-2y=47 \)

C). \( \Large x^{2}+y^{2}-2x+2y=47 \)

D). \( \Large x^{2}+y^{2}-2x+2y=62 \)

8). The pole of the straight line \( \Large x+2y=1 \) with respect to the circle \( \Large x^{2}+y^{2}=5 \) is:

A). \( \Large \left(5,\ 5\right) \)

B). \( \Large \left(5,\ 10\right) \)

C). \( \Large \left(10,\ 5\right) \)

D). \( \Large \left(10,\ 10\right) \)

9). If the circle \( \Large x^{2}+y^{2}+6x-2y+k=0 \) bisects the circumference of the circle \( \Large x^{2}+y^{2}+2x-6y-15=0 \) then k is equal to:

A). 21

B). -21

C). 23

D). -23

10). 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