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

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

ax² + 4xy + 2y² = 0 represents a pair of parallel lines then 'a' is _______.

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

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 combined equation of the given straight lines whose separate equations are 2x + y -1 = 0 and x + 2y -5 = 0.

Find the angle between the straight lines x² + 4xy + y² = 0

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

Show that the straight lines x + y - 4 = 0, 3x + 2 = 0 and 3x - 3y + 16 = 0 are concurrent

Find the value of 'a' for which the straight lines 3x + 4y = 13; 2x - 7y = -1  and ax - y - 14 = 0 are concurrent

Find the equation of the circle passing through the points (2, 3) and (-1, 1) and whose centre is on the line x-3y-11 = 0.

Show that the pair of straight lines 4x² - 12xy + 9y² + 18x - 27y + 8 = 0 represents a pair of parallel straight lines and find their separate equations.

For what values of a and b does the equation (a - 2)x² + by² + (b - 2)xy + 4x + 4y - 1 = 0 represents a circle? Write down the resulting equation of the circle.

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

If (4,1) is one extremity of a diameter of the circle x² + y² - 2x + 6y -15 = 0, find the other extremity.

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

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.