As the number of units manufactured increases from 6000 to 8000, the total cost of production increases from Rs. 33,000 to Rs. 40,000. Find the relationship between the cost (y) and the number of units made (x) if the relationship is linear.

Prove that the tangents to the circle x² + y²  = 169 at (5,12) and (12,-5) are perpendicular to each other.

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.

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How side is 2 m from the vertex of the parabola?