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

Ans:Hello Student,Please find answer to your question belowSlope of tangent:….........(1)Slope of tangent:…............(2)….......(3)Point of intersection

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Differential Calculus> Q. THE PARABOLAS Y 2 = 4AX AND X 2 = 4BY...

Q. THE PARABOLAS Y² = 4AX AND X² = 4BY INTERSECT ORHTOGONALLY AT POINT P(X₁, Y₁) WHERE X₁Y₁NOT EQUAL TO ZERO, PROVIDED-

B=A²

B=A³

B³=A²

NONE OF THESE

Bharat Makkar , 11 Years ago

Grade Select Grade

2 Answers

Jitender Singh

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
$(\frac{x^2}{4B})^2 = 4Ax$
$x^3 = 4^3AB^2$
$x = 4A^{1/3}B^{2/3}$
$y = \frac{x^2}{4B}$
$y = \frac{16A^{2/3}B^{4/3}}{4B}$
$y = 4A^{2/3}B^{1/3}$
$\frac{AA^{1/3}B^{2/3}}{BA^{2/3}B^{1/3}} = 1$
$A = B$