Question

已知抛物线y2=2px(p>0),点M(4,m)在抛物线上,若点M到抛物线焦点的距离为6.求抛物线方程及实数m的值

Answer 1

点M到焦点的距离为6 则 M 到准线的距离也是6

准线是 x = 4 - 6 =-2 = - p/2

p =4

抛物线方程是y^2 =8x

x=4时 y =±4√2

所以 m =±4√2