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 _______.

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

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

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

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

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 centre and radius of the circle x² + y² = 16

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

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

Find a point on x axis which is equidistant from the points (7, -6) and (3,4)

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 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 locus of a point which moves in such a way that the square of its distance from the point (3, -2) is numerically equal to its distance from the line 5x - 12y = 13

Prove that the lines 4x + 3y = 10, 3x - 4y = -5 and 5x + y = 7 are concurrent.

Prove that the tangents to the circle x² + y²  = 169 at (5,12) and (12,-5) are perpendicular to each other.

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How side is 2 m from the vertex of the parabola?

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