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The tangent at a point P on the curve x^4 y^5 = a^9 meet the x and y axes in A and B respectively Then AP:PB=?



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sauravshakya
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x^4 y^4 =a^9
d(x^4 y^4)/dx =d(a^9)/dx
d(x^4)/dx *y^4 + x^4 d(y^4)/dx =0
4x^3y^4 +x^4 4y^3 dy/dx=0
dy/dx =4x^3y^4/(4x^4y^3)
dy/dx =y/x

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Oh...No......There is a mistake in the question Sorry

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It is x^4 y^5 = a^9

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dy/dx = 4y/5x

sauravshakya
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x^4 y^5 =a^9
d(x^4 y^5)/dx =d(a^9)/dx
d(x^4)/dx *y^5 + x^4 d(y^5)/dx =0
4x^3y^5+x^4 5y^4 dy/dx=0
dy/dx =4x^3y^5/(5x^4y^4)
dy/dx =4y/5x

sauravshakya
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dw:1359203248993:dwNow, coordinate of P is

sauravshakya
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Now, can u?

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Now Using Distance Formula Ryt ( x ,0) (0,y)

sauravshakya
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U need to find coordinate of A and B

sauravshakya
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First find equation of tangent

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Then we have to find x and y intercept ryt ?