If m₁ and m₂ are the slopes of the pair of lines given by ax²+ 2hxy + by² = 0, then the value of m₁ + m₂ is _______.

(a)

2h/b

(b)

-2h/b

(c)

2h/a

(d)

-2h/a

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 locus of the point P which moves such that P is at equidistance from their coordinate axes is _______.

(a)

\(y={1\over x}\)

(b)

y = -x

(c)

y = x

(d)

\(y=-{1\over x}\)

The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is _______.

(a)

x+2y+2 = 0

(b)

x - 2y + 1 = 0

(c)

2x - y + 2 = 0

(d)

3x + y + 1 = 0

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

(1, - 2) is the centre of the circle x² + y² + ax + by - 4 = 0 , then its radius _______.

(a)

3

(b)

2

(c)

4

(d)

1

Length of the latus rectum of the parabola y² = - 25x is _______.

(a)

25

(b)

-5

(c)

5

(d)

-25

The centre of the circle x² + y - 2x + 2y - 9 = 0 is _______.

(a)

(1,1)

(b)

(-1,-1)

(c)

(-1,1)

(d)

(1, -1)

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

The double ordinate passing through the focus is _______.

(a)

focal chord

(b)

latus rectum

(c)

directrix

(d)

axis

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

(a)

a

(b)

2a

(c)

4a

(d)

3a

The equation of directrix of the parabola y² = - x is _______.

(a)

4x+ 1 =0

(b)

4x - 1 = 0

(c)

x - 4=0

(d)

x + 4 = 0

Find the centre and radius of the circle x² + y² = 16

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 equation of the circle whose centre is (2,3) and which passes through (1 , 4)

Find the equation of the circle passing through the points (0, 1) , (4 ,3) and (1, -1).

Find the equation of the circle on the line joining the points (1,0), (0,1) and having its centre on the line x + y = 1

A point moves so that its distance from the point (-1, 0) is always three times its distance from the point (0, 2). Find its locus.

For what value of \(\lambda \) are the three lines 2x-5y+3 = 0, 5x-9y+\(\lambda \)=0 and x-2y+1=0 are concurrent?

For what value of k does 12x² + 7xy + ky² + 13x - y + 3 = 0 represents a pair of straight lines?

Find the equation of a circle of radius 5 whose centre lies on X-axis and passes through the point (2, 3).

Find the equation of a circle whose diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area is 154 square units.

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

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