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Question

The equation of the normal to the hyperbola x2−9y2=7 at the point (4,1) is .

A
9x + 4y = 40
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B
9x - 4y = 40
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C
4x + 9y = 40
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D
4x - 9y = 40
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Solution

The correct option is A 9x + 4y = 40
Differentiating the equation of the hyperbola
x2−9y2=7 w.r.t x, we get− 2x−18ydydx=0or dydx=x9yNow the slope of a normal at any point on the curve is−dxdy=−9yxHence the slope of the normal at (4,1) is −94Hence, the equation of the normal is:y−1=−94(x−4)or 9x+4y=40

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