If A and B are the points (2, 3) and (4, -5) and P(x, y) is a point such that AP^ 2 − BP^ 2 = 8, show that x + y = 9.
PLS DONT SPAM.....
Answers
Answer:
9th
Maths
Circles
Equal Chords
If the chord of contact of ...
MATHS
avatar
Asked on December 20, 2019 by
Vedha Hariharan
If the chord of contact of tangents from a point on the circle x
2
+y
2
=a
2
to the circle x
2
+y
2
=b
2
touches the circle x
2
+y
2
=c
2
, then a,b,c are in
MEDIUM
Share
Study later
ANSWER
Let (x
1
,y
1
) be any point on the circle x
2
+y
2
=a
2
then, x
1
2
+y
1
2
=a
2
...(1)
Equation of chord of contact of tangents from (x
1
,y
1
) to the circle is xx
1
+yy
1
=b
2
...(2)
∵ (2) touches the circle x
2
+y
2
=c
2
∴ the length of ⊥ from center (0,0) on (2) is = radius =c
⇒
x
1
2
+y
1
2
b
2
=c⇒
a
2
b
2
=c⇒b
2
=ac
Hence, a,b,c are in G.P.
Answer:
Answer:
9th
Maths
Circles
Equal Chords
If the chord of contact of ...
MATHS
avatar
Asked on December 20, 2019 by
Vedha Hariharan
If the chord of contact of tangents from a point on the circle x
2
+y
2
=a
2
to the circle x
2
+y
2
=b
2
touches the circle x
2
+y
2
=c
2
, then a,b,c are in
MEDIUM
Share
Study later
ANSWER
Let (x
1
,y
1
) be any point on the circle x
2
+y
2
=a
2
then, x
1
2
+y
1
2
=a
2
...(1)
Equation of chord of contact of tangents from (x
1
,y
1
) to the circle is xx
1
+yy
1
=b
2
...(2)
∵ (2) touches the circle x
2
+y
2
=c
2
∴ the length of ⊥ from center (0,0) on (2) is = radius =c
⇒
x
1
2
+y
1
2
b
2
=c⇒
a
2
b
2
=c⇒b
2
=ac
Hence, a,b,c are in G.P.
plz follow and like