## Question

The equation of normal to the rectangular hyperbola *xy* = 4 at the point P on the hyperbola which is parallel to the line

2*x – y* = 5 is

### Solution

Slope of the normal to the rectangular hyperbola *xy* = 4 is m = *t*^{2} = 2 and 2*x – y* = 5 has slope = 2.

Equation of the normal is

⇒ *ty* – 2 = 2*t* (*x *– 2*t*)

⇒ *ty* – 2 = 2*tx* – 4*t*^{2}

⇒ 2*tx* – *ty* + 2 – 4*t*^{2} = 0

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