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.

2

(a)

A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.

2

(a)

If p is the length of perpendicular from the origin on the line \(\frac { x }{ a } +\frac { y }{ b } =1\) and a² , p² and b² are in AP, then show that a⁴ + b⁴ = 0. 

2

(a)

Find the equation of line passing through the point \((a\ { cos }^{ 3 }\theta ,\ a \ sin^{ 3 } \ \theta )\) and perpendicular to the line \(x \sec \theta+y \operatorname{cosec} \theta=a\) .

2

(a)

A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

2

(a)