y=0,x=-32/3。 One (-32/3,0)
x=0,y=8。 B(0,8)
(1) Find the coordinates of point p and the radius r of ⊙ p.
PB:kPB=- 1/k=-4/3
y=-4x/3+8
y=0,x=6,P(6,0)
Ob = 8, op = 6, and the circle centered on p is tangent to the straight line L at point B.
R=PB= 10
(2) If ⊙P moves to the left along the X axis at 3/ 10 units per second, and the radius of ⊙P decreases at 2/3 units per second, let ⊙P move for t seconds, and ⊙P always intersects with the straight line L, try to find the range of t;
R≥ the distance from point P to line L, then ⊙P always intersects with line L. 。
p,R= 10-2t/3,L:3x-4y+32=0
Distance from point P to line L H=| 10-9t/50|
10-2t/3≥|
10-2t/3≥ 10-9t/50≥-( 10-2t/3)
t≤0
There is something wrong with the topic. Try to change 3/ 10 to 10/3.
Distance from point P to line L: H=| 10-2t|
10-2t/3≥ 10-2t≥-( 10-2t/3)
7.5≥t≥0
(3) In (2), let ⊙P be cut by a straight line L with a chord length of A, and ask whether there is a value of t to maximize A? If it exists, find the value of t.
To maximize a, t must have a value.
(a/2)^2=r^2-h^2=( 10-2t/3)^2-( 10-2t)^2=(-32/9)*(t- 15/4)^2+50
T = 15/4,(a/2) 2 Max =50,a Max = 10√2。
(4) In (2), let the intersection of ⊙P and the straight line L be q, so that △APQ is similar to △ABO. Please write the value of t directly at this time.
△APQ is similar to△ △ABO, and PQ is perpendicular to AB.
⊙P is tangent to the straight line L.
T=0, or t=7.5