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 radius of the circle 3x² + by² + 4bx − 6by + b² = 0 is

(a)

1

(b)

3

(c)

\( \sqrt {10}\)

(d)

\( \sqrt {11}\)

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)

Equation of tangent at (-4, -4) on x² = -4y is _____________

(a)

2x - y + 4 = 0

(b)

2x + y - 4 = 0

(c)

2x - y - 12 = 0

(d)

2x + y + 4 = 0

y² - 2x - 2y + 5 = 0 is a _________

(a)

circle

(b)

parabola

(c)

ellipse

(d)

hyperbola

The locus of the point of intersection of perpendicular tangents of the parabola y² = 4ax is

(a)

latus rectum

(b)

directrix

(c)

tangent at the vertex

(d)

axis of the parabola

Focus of (y + 1)² = 8(x - 3)

(1)

8

Vertex of (y -1)² = 8x

(2)

4

LR of (y + 1)² = 8(x - 3)

(3)

(a, 0)

LR of (x - 4)² = 4(x + 2)

(4)

(0, 1)