The eccentricity of the ellipse (x−3)² +(y−4)² \(=\frac { { y }^{ 2 } }{ 9 } \) is

(a)

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

(b)

\(\frac { 1 }{ 3 } \)

(c)

\(\frac { 1 }{ 3\sqrt { 2 } } \)

(d)

\(\frac { 1 }{ \sqrt { 3 } } \)

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

The locus of a point whose distance from (-2,0) is \(\frac { 2 }{ 3 } \) times its distance from the line x = \(\frac { -9 }{ 2 } \) is

(a)

a parabola

(b)

a hyperbola

(c)

an ellipse

(d)

a circle

The values of m for which the line y = mx + \(2\sqrt { 5 } \) touches the hyperbola 16x² − 9y² = 144 are the roots of x² − (a + b)x − 4 = 0, then the value of (a+b) is

(a)

2

(b)

4

(c)

0

(d)

-2

If the coordinates at one end of a diameter of the circle x² + y² − 8x − 4y + c = 0 are (11, 2), the coordinates of the other end are

(a)

(-5, 2)

(b)

(-3, 2)

(c)

(5, -2)

(d)

(-2, 5)