In the rectangular coordinate system, O is the origin, and 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 Grade 8 Volume 2 exercise book people's education press 29 questions 10

In the rectangular coordinate system, O is the origin, and 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 Grade 8 Volume 2 exercise book people's education press 29 questions 10

1. K = XY substituting a (4,12) into k = 48
2. It's all right to draw. It's vertical
3. I don't have the following questions. The idea is
S=xy/2=k/2=48/2=24
4. If the distance between P and X axis is 6, that is y = 6, then x = 8, then p (8,6)
When the distance between P and Y axis is 6, that is, x = 6, y = 8, then p (6,8)

In the rectangular coordinate system, O is the origin of the coordinate, and the line y = - x + 6 intersects with the x-axis and y-axis at point a, and point B intersects with the hyperbola y = K / X at the first two points PQ
1. If ∠ AOP = 15 °, find the value of K

It is easy to get the coordinates of points a and B: a (6,0), B (0,6) simultaneous linear and hyperbolic equations, we can get - x + 6 = K / x, easy to solve x = 3 ± √ (9-k) ∧ point P coordinates may be P1 (3 - √ (9-k), 3 + √ (9-k)), P2 (3 + √ (9-k), 3 - √ (9-k)). For ∠ AOP, there is tan ∠ AOP = [K (OP) - K

The hyperbolic equation obtained by turning the curve X * y = 1 clockwise 45 degrees around the origin of the coordinate is

We can look at this problem in this way. If we rotate the hyperbola of the original problem by 45 degrees, it is a hyperbola with the focus on the y-axis, and other conditions remain unchanged
Hyperbola of Y ^ 2-x ^ 2 = 1

In the rectangular coordinate system, the coordinates of each vertex of the quadrilateral oabc are o (0,0), a (10,0), B (8,3), C (2,5)

Extend C and B to make the vertical line of X axis, the perpendicular foot D and e respectively
S four = s triangle OCD + s triangle EAB + s trapezoid cdeb = 32