A chord drawn 5 cm away from the center of a circle of radius 13 cm. Calculate the length of the chord?

Find the radius of a sphere whose surface area is 154 cm\(^2\)?

Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x = 0 and y = 0 (where k is a constant)?

What is the locus of the mid-point of all the chords of length 6cm with circle of radius 5cm and with center O?

What is the value of p if the gradient of the line joining (-1,p) and (p, 4) is \(\frac{2}{3}\)?