在平面直角坐标系xOy中,已知圆心在第二象限,半径为2 2 的圆C与直线y=x相切于坐标原点O.椭圆 x 2 a 2 + y 2 9 =1与圆C的一个交点到椭圆两焦点的距离之和为10. (1)C的方程; (2)试探求C上是否存在异于原点的点Q,使Q到椭圆右焦点F的距离等于线段OF的长.若存在,请求出点Q的坐标;若不存在,请说明理由.
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