Current location - Training Enrollment Network - Mathematics courses - Analytic geometry of high school mathematics competition
Analytic geometry of high school mathematics competition
I don't have a pen and paper on my computer, so I'll tell you the idea, and you can calculate it yourself according to the idea I gave you.

1。 2。 The problem of line intersection in quadrant is solved by two equations simultaneously.

X

Where's y

. Then.

The first quadrant is x>0.

Y>0, etc., you can get the parameters.

3。 The problem of a straight line passing through a fixed point: just substitute the straight line equation: y-a=k(x-b)

You can see that the fixed point (b, a) has passed.

4。

Bring in a=4/3b.

And then organize it into

Just look at the linear equation I gave in question 3.

5。 The linear equation passing through point P can be written as: y- 1=kx.

Assuming that the coordinates of M point are (a, b), according to the formula of midpoint coordinates, the coordinates of N point may be wrong.

Substitute the coordinates of point m into the equation x-3y+ 10=0.

N points are replaced by 2x+y-8=0.

Equation, you can calculate one.

,b

Because m is also in a straight line.

Substitute y- 1=kx.

It can be counted as K.