Question

ＱＵＥＳＴＩＯＮ-
If a point P moves such that the distance from the point A(1,1) and the line x+y+2=0 are equal then the locus of P is equal to​

Answer 1

Answer:

locus of p is ( x- y) 2 = 8 ( X+ Y ) which is a parabola

Answer 2

❥Answer:-

Let the coordinate at P is = (h,k)

∴ Distance com point A(1,1) is AP= (n−1) 2 +(k−1) 2

∴ Distance com line x+y+2=0 is = 1 2 +1 2

h+k+2

♡According to equation :-

• (h−1) 2 +(k−1) 2 = 2

h+k+2

Squaring both are:-

=2{(h−1) 2 +(k−1) 2 }

=(h+k+2) 2

⇒ 2(h 2 −2h+1+k 2 −2k+1)

=h 2 +k 2+4+2hk+4h+4k

⇒ 2h 2 −4h+2k 2 −4k+4

=h 2 +k 2 +4+2hk+4h+4k

⇒ h 2 −hk+k 2

=8h+4k

⇒ (h−k)

=8(h+k)

Locus of P is, (x−y) 2 =8(x+y) which is a parabola.

❥Hence Proved ✓