双曲线 试题 双曲线的中心在原点,焦点在x轴上,过双曲线右焦点且斜率为根号下15除以5的直线交双曲线于P,Q两点,若OP垂直于OQ,|PQ|=4,求双曲线方程

y=根号下15除以5(x-c)P(x1,根号下15除以5(x1-c))Q(x2,根号下15除以5(x2-c))x^/a^2-y^2/b^2=1x1^2-3(x1-c)^2/5=1x2^2-3(x2-c)^2/5=1OP^2=x1^2+3*(x1-c)^2/5OQ^2=x2^2+3*(x2-c)^2/5Op^2+OQ^2=PQ^2=16=x1^2+3*(x1-c)^2/...