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

Correct Answer:



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

Description for Correct answer:

The centre and radius of given circle are \( \Large \left(3,\ -2\right) \) and 5 respectively. The equation of a line parallel to \( \Large 4x+3y+5=0\ is\ 4x+3y+n=0 \)

As we know that perpendicular distance from centre \( \Large \left(3,\ -2\right) \) to the circle = radius of the circle.

\( \Large |\frac{4 \times 3+3 \times \left(-2\right)+n }{\sqrt{4^{2}+3^{2}}}| \)

\( \Large n = 19,\ -31 \) => Equation of tangents are

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

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

Comments

Similar Questions

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

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

3). 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

4). 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

5). 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

A). \( \Large x^{2}+y^{2}-2x-4y=0 \)

B). \( \Large x^{2}+y^{2}-2x-4y+3=0 \)

C). \( \Large x^{2}+y^{2}-2x-4y-3=0 \)

D). none of the above

6). 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). \( \Large \left(0,\ -1\right)\ and\ \left(0,\ -2\right) \)

7). 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

8). 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

9). 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

10). 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