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20 12 senior high school entrance examination mathematics
In the plane rectangular coordinate system XOY, the image of a linear function is a straight line l 1, which intersects the X axis and the Y axis at points A and B respectively. Line l2 passes through point C(a, 0) and is perpendicular to line l 1, where A > 0. Point P and point Q start from point A at the same time, where point P moves along ray AB. Point q moves along ray AO at a speed of 5 units per second.

(1) Write the coordinates of point A and the length of AB;

(2) When points P and Q move for several seconds, Q with point Q as the center and PQ as the radius is tangent to line l2 and Y axis, and the value of A at this time is found.

Test center: a function synthesis problem; The nature of tangent; Similar triangles's judgment and nature.

Special topic: geometric moving point problem; Classified discussion.

Analysis: (1) According to the intersection of the linear function image and the coordinate axis, the coordinates can be obtained separately;

(2) According to similar triangles's judgment, we get △APQ∽△AOB. When △ q is tangent to the right Y axis and △ q is tangent to the left Y axis, we get the answers respectively.

Solution: Solution: (1)∵ The image of a linear function is a straight line l 1, and l 1 intersects the X axis and the Y axis at points A and B respectively.

∴y=0,x = ? 4,

∴A(﹣4,0),AO=4,

∫ The coordinates of the intersection of the image and the Y axis are: (0,3), BO=3,

∴ab=5;

(2) From the meaning of the question: AP=4t, AQ=5t, = = t.

∠PAQ=∠OAB,

∴△APQ∽△AOB,

∴∠APQ=∠AOB=90,

Point p is on l 1

∴⊙Q keeps tangent to l 1 during the movement,

(1) When ⊙Q is tangent to the Y-axis on the right side of the Y-axis, let l2 and ⊙Q be tangent to F, and get from △APQ∽△AOB:

∴,

∴pq=6;

If QF is connected, QF=PQ, which consists of △QFC∽△APQ∽△AOB.

Have to,

∴,

∴,

∴QC=,

∴a=OQ+QC=OC=,

② When ⊙Q is tangent to the Y-axis on the left side of the Y-axis, let l2 and ⊙Q be tangent to E, from △APQ∽△AOB: =,

∴PQ=,

If QE is connected, QE=PQ is represented by △QEC∽△APQ∽△AOB: =,

∴=,=,

∴QC=,a=QC﹣OQ=,

∴a value is the sum,

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