No links please Chapter Name:TANGENT AND NORMAL22 In each of the following cases find the angle between the given - Maths - Differential Equations

Question

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C h a p t e r   N a m e : T A N G E N T   A N D   N
O R M A L 22   I n   e a c h   o f   t h e
  f o l l o w i n g   c a s e s   f i n d   t h
e   a n g l e   b e t w e e n   t h e   g i v e
n   c u r v e s :     i i   x 2 - y 2 = a 2
  a n d   x 2 + y 2 = 2 a 2 A n s ( i i )   π 4

Neha Sethi · Accepted Answer

Dear student
We have,x2-y2=a2  
1  and x2+y2=2a2  
2Adding 1 and 2, we get2x2=a2+2a22x2=a21+2x2=a21+22x=±a1+22Putting in 1 we geta21+22-y2=a2a21+2-2y2=2a2a2+a22-2y2=2a2a22-2y2-a2=02y2=a22-a2y2=a22-12y=±a2-12Differenciating 1 w
r t
 x, we get2x-2ydydx=0x-ydydx=0ydydx=xdydx±a1+22,±a2-12=xy=±a1+22±a2-12=1+22-1=m1Differenciating 2 w
r t
 x, we get2x+2ydydx=0x+ydydx=0ydydx=-xdydx=-xydydx±a1+22,±a2-12=-xy=-±a1+22±a2-12=-1+22-1=m2Let θ be the angle of intersection of 1 and 2 ,thentanθ=m1-m21+m1m2=1+22-1+1+22-11+1+22-1-1+22-1=21+22-1-1-2θ=tan-121+22-1-1-2Please recheck the answer
Regards

No links please C h a p t e r N a m e : T A N G E N T A N D N O R M A L 22 . I n e a c h o f t h e f o l l o w i n g c a s e s f i n d t h e a n g l e b e t w e e n t h e g i v e n c u r v e s : i i x 2 - y 2 = a 2 a n d x 2 + y 2 = 2 a 2 A n s ( i i ) π 4

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$C h a p t e r N a m e : T A N G E N T A N D N O R M A L 22 . I n e a c h o f t h e f o l l o w i n g c a s e s f i n d t h e a n g l e b e t w e e n t h e g i v e n c u r v e s : (i i) x^{2} - y^{2} = a^{2} a n d x^{2} + y^{2} = \sqrt{2} a^{2} A n s (i i) \frac{π}{4}$