The equation of the locus of a point equidistant from the points (a, b) and (c, d) is (a - c)  x + (b - d)  y + k = 0 What is the value of k?

Consider the following statements in respect of the equation $x ^ 2 + 3y = 0$

I. The equation represents the equation to parabola that opens upwards.

II. The axis of the parabola is x = 0

III. The equation of the latus rectum is 4y - 3 = 0

How many of the statements given above are correct?

What is the sum of the intercepts of the line
$\frac{x}{a^{2}}+\frac{y}{b^{2}}=\frac{2}{a^{2}+b^{2}} $ on the coordinate axes?

Which one of the following is the perpendicular form of the straight line $\sqrt{3}x+2y=7$ ?