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The square of the length of the tangent from \( \Large \left(3,\ -4\right) \) to the circle \( \Large x^{2}+y^{2}-4x-6y+3=0 \) is:

A) 20
B) 30
C) 40
D) 50

Correct Answer:



C) 40

Description for Correct answer:

Length of tangent from the point \( \Large \left(x_{1},y_{1}\right) \) to the circle \( \Large x^{2} + y^{2} +2gx + 2fy + c = 0 \) is

\( \Large \sqrt{x_{1}^{2} +y_{1}^{2} + 2gx_{1} + 2fy_{1} + c } \)
Required length of tangent from the point (3,-4) to the circle \( \Large x^{2} + y^{2} -4x -6y + 3 = 0 \)

\( \Large \sqrt{3^{2} + 4^{2} + -4(3) - 6(-4) + 3} = \sqrt{40}\)
Square of the length of tangenet is 40

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

Comments

Similar Questions

1). If \( \Large g^{2}+f^{2}=c \) then the equation \( \Large x^{2}+y^{2}+2gx+2fy+c=0 \) will represent:

A). a Circle of radius g

B). a circle of radius f

C). a circle of diameter \( \Large \sqrt{c} \)

D). a circle of radius 0

2). The limit of the perimeter of the regular n polygons inscribe in a circle of radius R as \( \Large n\ \rightarrow\ \infty \) is:

A). \( \Large 2 \pi R \)

B). \( \Large \pi R \)

C). \( \Large 4R \)

D). \( \Large \pi R^{2} \)

3). The value of n, for which the circle \( \Large x^{2}+y^{2}+2nx+6y+1=0 \) intersects the circle \( \Large x^{2}+y^{2}+4x+2y=0 \) orthogonally is:

A). \( \Large \frac{11}{8} \)

B). -1

C). \( \Large \frac{-5}{4} \)

D). \( \Large \frac{5}{2} \)

4). 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

5). 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

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

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

8). 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

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

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