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)

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

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is _______.

(a)

(-1, 1)

(b)

(1,1)

(c)

(1, -1 )

(d)

(-1, -1)

The x-intercept of the straight line 3x + 2y - 1 = 0 is _______.

(a)

3

(b)

2

(c)

1/3

(d)

1/2

If the centre of the circle is (-a, -b) and radius is \(\sqrt{a^2-b^2}\), then the equation of circle is _______.

(a)

x²+y²+2ax+2by+2b² = 0

(b)

x²+y²+2ax +2by-2b² = 0

(c)

x² +y² - 2ax - 2by - 2b² = 0

(d)

x² + y - 2ax - 2by + 2b² = 0

Combined equation of co-ordinate axes is _______.

(a)

x²-y² = 0

(b)

x²+y² = 0

(c)

xy = c

(d)

xy = 0

If the perimeter of the circle is 8π units and centre is (2, 2) then the equation of the circle is _______.

(a)

(x - 2)² + (y - 2)² = 4

(b)

(x - 2)² + (y - 2)² = 16

(c)

(x - 4)² + (y - 4)² = 2

(d)

x² + y² =4

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

If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is _______.

(a)

6

(b)

3

(c)

12

(d)

4

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

If A (-1,1) and B (2,3) are two fixed points, then find the locus of a point P So that the area of triangle APB = 8 Sq.units

Find the equation of the following circles having the centre (3,5) and radius 5 units

Find the equation of the following circles having the centre (0,0) and radius 2 units

Find the center and radius of the circle  x² + y² - 22x - 4y + 25 = 0

Find the center and radius of the circle 5x² + 5y² + 4x - 8y - 16 = 0

Find the focus, equation of the directrix, vertrix and length of latus sections of the parabola x²=6y.

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

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16, find its locus.

Prove that the lines (b - c) x + (c - a) y + (a - b) = 0, (c - a) x + (a - b) y + (b - c) = 0, and (a - b) x + (b - c) y+c-a=0 are concurrent.

Find the slope of the lines which make an angle of 45° with the line 3x - y + 5 = 0.

Find the combined equation of the straight line through the origin, one of which is parallel to and the other is perpendicular to the straight line 2x + y + 1 = 0

Find the equation of the circle having centre at (3, -4) and touching the line 5x + 12y - 12 = 0

Show that the pair of straight lines 4x² +12xy + 9y² -6x -9y +2 = 0 represents two parallel straight lines and also find the separate equations of the straight lines.

Find the angle between the pair of straight lines 3x² - 5xy - 2y² + 17x + y + 10 = 0