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 equation of the normal to the circle x² + y² − 2x − 2y + 1 = 0 which is parallel to the line 2x + 4y = 3 is

(a)

x + 2y = 3

(b)

x + 2y + 3 = 0

(c)

2x + 4y + 3 = 0

(d)

x − 2y + 3 = 0

If the normals of the parabola y² = 4x drawn at the end points of its latus rectum are tangents to the circle (x − 3)² + (y + 2)² = r² , then the value of r² is

(a)

2

(b)

3

(c)

1

(d)

4

The equation of the circle passing through the foci of the ellipse  \(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\) having centre at (0, 3) is

(a)

x² + y² − 6y − 7 = 0

(b)

x² + y² − 6y + 7 = 0

(c)

x²+y²−6y−5 = 0

(d)

x²+y²−6y+5 = 0

If the two tangents drawn from a point P to the parabola y² = 4x are at right angles then the locus of P is

(a)

2x + 1 = 0

(b)

x = −1

(c)

2x −1 = 0

(d)

x = 1

If (0, 4) and (0, 2) are the vertex and focus of a parabola then its equation is ___________

(a)

x² + 8y = 32

(b)

y² + 8x = 32

(c)

x² - 8y = 32

(d)

y² - 8x = 32

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

In an ellipse, the distance between its foci is 6 and its minor axis is 8, then e is ________

(a)

\(\frac { 4 }{ 5 } \)

(b)

\(\frac { 1 }{ \sqrt { 52 } } \)

(c)

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

(d)

\(\frac { 1 }{ 2 } \)

The number of normals that can be drawn from a point to the parabola y² = 4ax is __________

(a)

3

(b)

2

(c)

0

(d)

1