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​Q. THE PARABOLAS Y 2 = 4AX AND X 2 = 4BY INTERSECT ORHTOGONALLY AT POINT P(X 1 , Y 1 ) WHERE X 1 Y 1 NOT EQUAL TO ZERO, PROVIDED- B=A 2 B=A 3 B 3 =A 2 NONE OF THESE

​Q. THE PARABOLAS Y2 = 4AX AND X2 = 4BY INTERSECT ORHTOGONALLY AT POINT P(X1 , Y1) WHERE X1Y1 NOT EQUAL TO ZERO, PROVIDED-
  1. B=A2
  2. B=A3
  3. B3=A2
  4. NONE OF THESE

Grade:Select Grade

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

y^2 = 4Ax
Slope of tangent:
2yy' = 4A
y' = -\frac{2A}{y}….........(1)
x^2 = 4By
Slope of tangent:
y' = \frac{x}{2B}…............(2)
(1)\times (2) = -1
\frac{Ax}{By} = 1….......(3)
Point of intersection
(\frac{x^2}{4B})^2 = 4Ax
x^3 = 4^3AB^2
x = 4A^{1/3}B^{2/3}
y = \frac{x^2}{4B}
y = \frac{16A^{2/3}B^{4/3}}{4B}
y = 4A^{2/3}B^{1/3}
\frac{AA^{1/3}B^{2/3}}{BA^{2/3}B^{1/3}} = 1
A = B
Bharat Makkar
34 Points
9 years ago
THANK YOU VERY MUCH SIR FOR ALL THE ANSWERS........

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