Find the length of the tangent from(3,4) to the circle 2x² +2y²+3x-4y+7=0
Answers
Answered by
2
Answer:
Center of the circle is (43,1)
Distance of point B from the center of the circle is 2−43=45
The radius of the circle is given by (43)2+(1)2=(45)
Since distance between point B and the center of the circle equals the radius and a tangent touches the circle at only one point, A has to coincide with B.
∴AB=0
Answered by
0
Answer:
Tofindthecentreandradiusofcentre
2x
2
+2y
2
=3x−5y+7
2x
2
+2y
2
−3x+5y=7
x
2
+y
2
−
2
3
x+
2
5
y=
2
7
(
devided
by2
)
x
2
−
2
3
x+y
2
+
2
5
y=
2
7
x
2
−
2
3
x+
16
9
+y
2
+
2
5
y+
16
25
=
2
7
+
16
9
+
16
25
(x−
4
3
)
2
+(y+
4
5
)
2
=
2
7
+
16
9
+
16
25
=
2
7
+
16
34
=
16
90
⇒(x−
4
3
)
2
+(y+
4
5
)
2
=
16
90
Comparingwithgeneralequation
h=
4
3
,k=
4
−5
,r=
16
9
(h,k)=(
4
3
,
4
−5
)r=
4
90
Ans.
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