(AUB)'=A'(intersection)B' is....
Answers
Step-by-step explanation:
A point of intersection of
List 1
x
2
+y
2
=9
and
y
2
=8x
is
2
x
2
+
16
y
2
=1
and
y
2
=8x
is
4
x
2
−
1
y
2
=1
and
16
x
2
+
2
y
2
=1
is
4
x
2
−
1
y
2
=1
and
x
2
=−8y
is
List 2
(1,2
2
)
(1,−2
2
)
(2
2
,−1)
(−2
2
,−1)
Hard
Solution
verified
Verified by Toppr
A) Substituting y
2
=8x in x
2
+y
2
=9⇒x
2
+8x−9=0⇒(x−1)(x+9)=0
For x=1y
2
=8⇒y=±2
2
And for x=−9y
2
=−8.9
Hence intersection point is (1,2
2
) and (1,−2
2
)
B) Substituting y
2
=8x in
2
x
2
+
16
y
2
=1⇒x
2
+x=2⇒(x+2)(x−1)=0
For x=−2y
2
=−8.2
And for x=1y
2
=8⇒y=±2
2
Hence intersection point is (1,2
2
)(1,−2
2
)
C)
4
x
2
−
1
y
2
=1⇒x
2
=4+4y
2
substituting this in
16
x
2
+
2
y
2
=1⇒y
2
=1
We get
y=±1,x=±2
2
Hence intersection point are
(2
2
,+1),(2
2
,−1),(−2
2
,+1)(−2
2
,−1)
D) Substituting x
2
=−8y in
4
x
2
−
1
y
2
=1⇒y
2
+2y+1=0⇒(y+1)
2
=0
y=−1,x=±2
2
Hence intersection points are
(−2
2
,−1),(2
2
,−1)