another point (h,k) without
changing the direction of
the axes is called
Answers
Answer:
Answer
Let the origin be shifted to (h,k)
(a) ⇒x=X+h,y=Y+k
Given equation →x
2
+y
2
+4x−6y−3=0
⇒(X+h)
2
+(Y+k)
2
+4(X+h)−6(Y+k)−3=0
⇒X
2
+h
2
+2hX+Y
2
+k
2
+2kY+4X+4h−6Y−6k−3=0
⇒X
2
+Y
2
+(2h+4)X+(2k−6)Y+(h
2
+k
2
+4h−6k−3)=0
Given that equation is transformed as X
2
+Y
2
=a
2
Therefore, ⇒2h+4=0 ⇒h=−2
⇒2k−6=0 ⇒k=3
⇒h
2
+k
2
+4h−6k−3=−a
2
⇒(−2)
2
+3
2
+4(−2)−6(3)−3=−a
2
⇒a
2
=16
Thus, the transformed equation is x
2
+y
2
=16
(b) ⇒x=X+h,y=Y+k
Given equation →y
2
−3x+4y+13=0
⇒(Y+k)
2
−3(X+h)+4(Y+k)+13=0
⇒Y
2
+k
2
+2kY−3X−3h+4Y+4k+13=0
⇒Y
2
−3X+(2k+4)Y+(k
2
−3h+4k+13)=0
Given that equation is transformed as Y
2
=aX
Therefore, ⇒2k+4=0 ⇒k=−2
⇒k
2
−3h+4k+13=0
⇒(−2)
2
−3h+4(−2)+13=0
⇒3h=9 ⇒h=3
Thus, the transformed equation is y
2
=−3x
Explanation:
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