then Let P(x1,y1) be any point, √(x1−0)2+(y1−2)2+√(x1−0)2+(y1+2)2=6 ⇒√x12+(y1−2)2=6−√x12+(y1+2)2 ⇒x12+(y1−2)2=36+(x12+(y1+2)2)−12√x12+(y1+2)2 ⇒−8y1=36−12√x12+(y1+2)2 ⇒3√x12+(y1+2)2=2y1+9 ⇒9(x12+(y1+2)2)=4y12+81+36y1 ⇒9x12+5y12=45 Hence, locus of a point is 9x2+5y2=45