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

Correct Answer:



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

Description for Correct answer:

The equation of diameters are

\( \Large 2x-3y = 5 \) ...(i)

and \( \Large 3x-4y = 7 \) ...(ii)

On solving eqs. (i) and (ii) we get

\( \Large x = 1\ and\ y = -1 \)

Therefore, Centre of circle = \( \Large \left(1,\ -1\right) \)

Since area of circle is 154 sq unit then radius of circle r = 7

Equation of circle is \( \Large \left(x-1\right)^{2}+ \left(y+1\right)^{2} = 49 \)

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

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

Comments

Similar Questions

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

2). 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

3). 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

4). 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

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

6). 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

7). 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

8). 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

9). 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

10). 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