for what values of p does the vertex of the parabola y=x2+ 2px+13 lies at a distance of 5 from - Maths - Complex Numbers and Quadratic Equations

Question

for what values of p does the vertex of the parabola y=x2+
2px+13 lies at a distance of 5 from the origin

Ajanta Trivedi · Accepted Answer

the given equation of the parabola is : y=x2+2px+13
y=x2+2px+p2-p2+13y-(13-p2)=(x+p)2comparing the equation with
(x-h)2=4a(y-k)the vertex of the parabola are (-p,13-p2)
if the distance of the vertex from the origin is 5
then
(p-0)2+(13-p2)2=52p2+169+p4-26p2=25p4-25p2+144=0p4-16p2-9p2+144=0p2(p2-16)-9(p2-16)=0(p2-16)(p2-9)=0⇒p2=16
or p2=9⇒p=±4 or p=±3therefore p=4,-4,3,-3

hope this helps you

for what values of p does the vertex of the parabola y=x2+ 2px+13 lies at a distance of 5 from the origin