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 _______.

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

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

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

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

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

If the lines x + y = 6 and x + 2y = 4 are diameters of the circle, and the circle passes through the point (2, 6)  then find its equation.

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.

If the centre of the circle x² + y² + 2x - 6y + 1 = 0 lies on a straight line ax + 2y + 2 = 0, then find the value of ‘a’

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

Find whether the points (-1,-2), (1,0) and (-3, -4) lie above, below or on the line 3x + 2y + 7 = 0.

Show that the equation 2x² + 7xy + 3y² + 5x + 5y + 2 = 0 represent two straight lines and find their separate equations.