The angle between the pair of straight lines x² - 7xy + 4y² = 0 _______.

(a)

\(tan^{-1}\left(1\over 3\right)\)

(b)

\(tan^{-1}\left(1\over 2\right)\)

(c)

\(tan^{-1}\left(\sqrt{33}\over 5\right)\)

(d)

\(tan^{-1}\left(5\over\sqrt{33}\right)\)

The slope of the line 7x + 5y - 8 = 0 is _______.

(a)

7/5

(b)

-7/5

(c)

5/7

(d)

-9/7

If kx² + 3xy - 2y² = 0 represent a pair of lines which are perpendicular then k is equal to _______.

(a)

1/2

(b)

-1/2

(c)

2

(d)

-2

The length of the tangent from (4,5) to the  circle x² + y² = 16 is _______.

(a)

4

(b)

5

(c)

16

(d)

25

The focus of the parabola x² = 16y is _______.

(a)

(4,0)

(b)

(-4,0)

(c)

(0,4)

(d)

(0,-4)

Combined equation of co-ordinate axes is _______.

(a)

x²-y² = 0

(b)

x²+y² = 0

(c)

xy = c

(d)

xy = 0

In the equation of the circle x² + y² = 16 then y intercept is (are) _______.

(a)

4

(b)

16

(c)

±4

(d)

±16

The equation of the circle with centre (3,-4) and touches the x - axis is _______.

(a)

(x - 3)² +(y - 4)² = 4

(b)

(x - 3)² +(y + 4)² = 16

(c)

(x-3)² + (y- 4)² = 16

(d)

x²+y² = 16

The eccentricity of the parabola is _______.

(a)

3

(b)

2

(c)

0

(d)

1

The distance between directrix and focus of a parabola y² = 4ax is _______.

(a)

a

(b)

2a

(c)

4a

(d)

3a

Find the equation of the circle whose centre is (-3, -2) and having circumferences 16\(\pi\)

Find the acute angle between the lines 2x - y + 3 = 0 and x + y + 2 = 0.

Find the angle between the pair of lines represented by the equation 3x²+10xy+8y²+14x+22y+15=0.

For what value of k does 2x² + 5xy + 2y² + 15x + 18y + k = 0 represent a pair of straight lines.

Find the parametric equations of the circle x² + y² = 25

Find the angle between the lines whose slopes are \(\frac { 1 }{ 2 } \) and 3

The parabola y² = Kx passes through the point (4, -2) find its latus rectum and focus.

Find the equation of the parabola whose focus is (-3, 2) and the directrix is x + y = 4.

Find the equation of the tangent lines to the circle x² + y² = 9 which are parallel to 2x + y - 3 = 0

If the equation of a circle x² + y² + ax + by = 0 passing through the points (1, 2) and (1, 1), find the values of a and b

Find the value of p for which the straight lines 8px + (2 - 3p)y + 1 = 0 and px + py - 7 = 0 are perpendicular to each other.

Find the equation of the parabola whose vertex is (0, 0) passing through the point (2, 3) and axis is along X-axis.

Find the equation of the parabola whose focus is (1,3) and whose directrix is x - y + 2 = 0.