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Question: A line L is perpendicular to the curve y = \(\frac{x^{2}}{4}\)– 2 at its point P and passes through ...

A line L is perpendicular to the curve y = x24\frac{x^{2}}{4}– 2 at its point P and passes through (10, –1). The coordinates of the point P are-

A

(2, –1)

B

(6, 7)

C

(0, –2)

D

(4, 2)

Answer

(4, 2)

Explanation

Solution

Let the point is (h,h2−84)\left( h,\frac{h^{2} - 8}{4} \right); equation of normal

(y−h2−84)\left( y - \frac{h^{2} - 8}{4} \right)= −2h\frac{- 2}{h} (x – h);

Q (10, –1) lies on it h3 + 4h – 80 = 0