Question

设P(x0,y0)为抛物线y^2=4x上的一点,点F为抛物线的焦点,以点F为圆心...

设P(x0,y0)为抛物线y^2=4x上的一点,点F为抛物线的焦点,以点F为圆心,以|PF|为半径的圆与抛物线的准线相离,求x0的取值范围

Answer 1

y²
=
4x
=
2px,p
=
2
F(1,0),准线x
=
-1,二者相距2,即抛物线在以F为圆心,2为半径的圆内的部份均满足条件.
圆:(x
-
1)²
+
y²
=
4
(x
-
1)²
+
4x
=
4
x²
+
2x
-
3
=
0
(x
+
3)(x
-
1)
=
0
x
=
1
(舍去x
=
-3
<
0)
0
≤
x0