The question given below consist of an assertion (A) and the reason ( R) use the following key to choose the appropriate answer.
A: The product of the ordinates of the point of tangency to the curve $(1 + x^{2}) y = 2 - x$ , where the tangent makes equal intercept with coordinate axes is equal to 1.
R: Slope of straight line making equal and same sign intercept with coordinate axes is equal to -1

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If both assertion and reason are correct but reason is not correct explanation of the assertion

If both assertion and reason are correct and reason is the correct explanation of the assertion

If assertion is incorrect, but reason is correct

If assertion is correct but reason is incorrect

answer is A.

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Detailed Solution

Clearly reason is correct

$(1 + x^{2}) y = 2 - x$ Differentiating w.r.t. x
$(1 + x^{2}) \frac{d y}{d x} + 2 x y = - 1 Put \frac{d y}{d x} = - 1 \Rightarrow x = 0 or 2 y = x When x = 0, y = 2$
When $x = 2 y \Rightarrow 4 y^{3} + 3 y - 2 = 0 \Rightarrow y = \frac{1}{2}$ only real root
$∴ Product of ordinates$ $= 2 \cdot \frac{1}{2} = 1$