Question

Find the equation to the locus of the point p if the sum of squares of its distance from (1,2)and(3,4)is 25 units

Answer 1

Answer:

$2(p-2)^2+(q-6)^2=39$

Step-by-step explanation:

1) Now,

Let the point be P(p,q).

Then, According to the question,

Sum of squares of its distance from (1,2) and (3,4) is 25 units.

That is,

$(p-1)^2+(q-2)^2+(p-3)^2+(q-4)^2=25\\ \\=>p^2-2p+1+q^2-4q+4+p^2-6p+9+q^2-8q+16=25\\ \\=>2p^2-8p+q^2-12q+30=25\\ \\=>2p^2-8p+q^2-12q+5=0\\ \\=>2(p-2)^2+(q-6)^2=39\\ \\=>\frac{(p-2)^2}{39/2}+\frac{(q-6)^2}{39}=1$

Above equation is that of ellipse , with unequal major and minor axis length.

Length of Minor axis of ellipse : $\sqrt{\frac{39}{2}}units$

Length of Major axis of ellipse:$\sqrt{39}\:units$

Answer 2

the answer to your question is below:

2(p−2) 2 +(q−6) 2=39