Question

A straight line parallel to the line 2x - y + 5 = 0 is also a tangent to the curve $y^{2}=4x+5.$ Then the point of contact is

• A. (2,1)
• B. (-1,1)
• C. (1,3)
• D. (3,4)

Answer 1

Answer: (B)

(-1,1)

Answer 2

Given curve is $y^{2}=4x+5.$ on differentiating, we get $2 y \frac{d y}{d x}=4 \, \Rightarrow\quad\frac{d y}{d x}=\frac{2}{y}$ Given line is 2x - y + 5 = 0 $\Rightarrow\, y=2x+5$ slope of line is 2. Therefore, $\frac{2}{y}=2 \Rightarrow y=1$ put y = 1 in the equation of curve, we get 1 = 4x + 5 x = - 1 Hence, point of contact is (- 1, 1)