JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q77

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MathematicsSingle correct+4 / -1Question 77 of 90

A tangent to the curve, $y=f(x)$ at P(x, y) meets $x$ -axis at A and $y$ -axis at B. If AP : BP = 1 : 3 and $f(1)=1$ , then the curve also passes through the point :

\left(\dfrac13,24\right)

\left(\dfrac12,4\right)

\left(2,\dfrac18\right)

\left(3,\dfrac1{28}\right)

Answer and worked solution

Official answer: C

The tangent meets the axes at $A=\left(x-\frac y{y'},0\right)$ and $B=(0,y-xy')$ . AP : PB = 1 : 3 gives $x=\frac34\left(x-\frac y{y'}\right)$ , so $y'=-\frac{3y}x$ and $y=\frac c{x^3}$ . With $f(1)=1$ , $y=\frac1{x^3}$ , which passes through $\left(2,\frac18\right)$ .

Topics:Variable separable Tangents and normals

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JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 77