The equation of the circle passing through (1, 5) and (4, 1) and touching y-axis is x² + y² − 5x − 6y + 9 + \(\lambda\)(4x + 3y − 19) = 0 where λ is equal to

(a)

\(0,-\frac { 40 }{ 9 } \)

(b)

0

(c)

\(\frac { 40 }{ 9 } \)

(d)

\(\frac { -40 }{ 9 } \)

The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

(a)

\(\frac { 4 }{ 3 } \)

(b)

\(\frac { 4 }{ \sqrt { 3 } } \)

(c)

\(\frac { 2 }{ \sqrt { 3 } } \)

(d)

\(\frac { 3 }{ 2 } \)

The circle x² + y² = 4x + 8y +5 intersects the line 3x−4y = m at two distinct points if

(a)

15< m < 65

(b)

35< m <85

(c)

−85 < m < −35

(d)

−35 < m < 15

The length of the diameter of the circle which touches the x - axis at the point (1, 0) and passes through the point (2, 3).

(a)

\(\frac { 6 }{ 5 } \)

(b)

\(\frac { 5 }{ 3 } \)

(c)

\(\frac { 10 }{ 3 } \)

(d)

\(\frac { 3 }{ 5 } \)

The centre of the circle inscribed in a square formed by the lines x² − 8x − 12 = 0 and y² − 14y + 45 = 0 is

(a)

(4, 7)

(b)

(7, 4)

(c)

(9, 4)

(d)

(4, 9)