If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are x = a cos³ θ, y = a sin³ θ.

A straight rod of length 8 units slides with its ends A and B always on the x and y axes respectively. Find the locus of the mid point of the line segment AB.

Find the equation of the locus of a point such that the sum of the squares of the distance from the points (3, 5), (1, -1) is equal to 20.

Find the equation of the locus of the point P such that the line segment AB, joining the points A(1, -6) and B(4,-2), subtends a right angle at P.

lf P(2,-7) is a given point and Q is a point on (2x² + 9y² = 18), then find the equations of the locus of the mid-point of PQ.

If Q is a point on the locus of x² + y²+ 4x - 3y + 7 = 0, then find the equation of locus of P which divides segment OQ externally in the ratio 3 : 4, where O is origin.

The sum of the distance of a moving point from the points (4, 0) and (-4, 0) is always 10 units. Find the equation to the locus of the moving point.

The normal boiling point of water is 100°C or 212°F· and the freezing point of water is 0 °C or 32°F.
(i) Find the linear relationship between C and F.
(ii) Find the value of C for 98.6°F and 
(iii) Find the value of F for 38°C.

An object was launched from a place P in constant speed to hit a target. At the 15th second it was1400m away from the target and at the 18th second 800m away. Find 
(i) the distance between the place and the target.
(ii) the distance covered by it in 15 seconds.
(iii) time taken to hit the target.

A ray of light coming from the point (1, 2)is reflected at a point A on the x-axis and it passes through the point (5, 3). Find the co-ordinates of the point A.