It is known that the lengths of the two right angles of a right triangle are a and B respectively, and the lengths of the hypotenuse are C, and a, B and C are all positive integers, where a is a prime. It is proved that 2 (a + B + 1) = (a + 1) & sup2;

How many common points do hyperbola y = K / X and straight line y = - KX have?

0,
When k is greater than 0, the hyperbola y = K / X is in the first and third quadrants, and the straight line y = - KX passes through the origin in the second and fourth quadrants
When k is less than 0, the hyperbola y = K / X is in the second and fourth quadrants, the straight line y = - KX passes through the origin in the first and third quadrants, and there is no intersection between the hyperbola and the straight line
In conclusion, the common points of hyperbola y = K / X and straight line y = - KX are 0

When k > 0, what is the common point of hyperbola y = K / X and straight line y = - KX?

At the same time, we get k / x = - KX
So x ^ 2 = - 1
Obviously not, so there is no intersection
In fact, if K is less than 0, two curves have no intersection

As shown in the figure, in the rectangular coordinate system, O is the origin, and the point a (4,12) is the point on the hyperbola y = x / K (x is greater than 0)
(1) Finding the value of K
(2) Through the point P on the hyperbola, make Pb perpendicular to the x-axis and connect Op
(3) Finding the area of RT triangle OPB
(4) If one of the distances between point P and x-axis or y-axis is 6, the coordinates of point P are obtained

There is no picture. How to do it? It should be very simple. I've done a similar raising k = 4 * 12 = 48

It is known that the lengths of the two right angles of a right triangle are a and B respectively, and the lengths of the hypotenuse are C, and a, B and C are all positive integers, where a is a prime. It is proved that 2 (a + B + 1) = (a + 1) & sup2;