The circle is
(x-2)^2 + (y-1)^2 = 25
The shortest distance is along the line from the center (2,1) to (10,7). So, find the distance between those two points, and subtract 5, the radius of the circle. For the longest distance add 5, to the opposite end of the diameter.
The runner rests at the end of the hypotenuse of a 3-4-5 triangle. You give no indication of the finish point.
The parabola has the equation
y = 18-kx^2
Since the point (32,10) is on the parabola, the equation is
y = 18 - 1/128 x^2
The roots are ±48
so the width at the bottom is 96m
1. Find the longest and shortest distance from (10, 7) to the circle x^2 + y^2-4x-2y-20=0
2. From the start, a man runs 4km towards north, 3 km towards east and takes a rest. Draw the line from starring point to resting point and line from resting point to finish point. Find the angle between the lines assuming that east-west is parallel to x-axis.
3. And arch 18months high has the form of a parabola with a vertical axis. The length of a horizontal beam placed across the arch 8m from the top is 64m. Find the width of the arch at the bottom.
1 answer
1 answer