Show that two tangents can be drawn from the point (9,0) to the circle x square + y square is equal to 16 also find the equation of the pair of tangents and the angle between them.
Answers
Answered by
1
Ans. Equation of the circle x
2
+y
2
=16
Center, C=(0,0) and Radius, r=4
Distance between (9,0) and (0,0),
d=
(0−9)
2
+(0−0)
2
=(
9
)
2
=9
d=9>r
since the point lies outside the circle.
∴ Two tangents can be drawn from (9,0) to the circle.
Equation of tangent to the circle x
2
+y
2
=0 is,
y=mx±a(
1+m
2
)
y−mx=±a(
1+m
2
)
Squaring both sides,
(y−mx)
2
=(±a(
1+m
2
))
2
(y−mx)
2
=a
2
(
1+m
2
)
2
a=4, substituting
(y−mx)
2
=4
2
(1+m
2
)
∴(y−mx)
2
=16(1+m
2
)
This line passes through (9,0),
Put, x=9 and y=0
(−9m)
2
=16+16m
2
81m
2
−16m
2
=16
65m
2
=16
m=
65
16
=±
65
4
m
1
=+
65
4
, m
2
=−
65
4
m
1
+m
2
=0
Similar questions