Question

The line $x - y + 2 = 0$ touches the parabola $y ^ { 2 } = 8 x$ at the point

• A. (2, –4)
• B. $( 1,2 \sqrt { 2 } )$
• C. $( 4 , - 4 \sqrt { 2 } )$
• D. (2, 4)

Answer 1

Answer: (D)

(2, 4)

Answer 2

The line $x - y + 2 = 0$ i.e. $x = y - 2$ meets parabola $y ^ { 2 } = 8 x$ if

$\Rightarrow y ^ { 2 } = 8 ( y - 2 ) = 8 y - 16$ ⇒ $( y - 4 ) ^ { 2 } = 0$

⇒ $y = 4,4$

$\bullet \bullet$ Roots are equal, ∴ Given line touches the given parabola.

∴ $x = 4 - 2 = 2$ , Thus the required point is (2, 4)