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  • The line   touches the parabola <img alt="\mathrm{ y^2=8 x}" src="https://

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

Option: 1

(2,-4)


Option: 2

(1,2 \sqrt{2})


Option: 3

(4,-4 \sqrt{2})


Option: 4

(2,4)


Answers (1)

best_answer

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

\mathrm{ \Rightarrow y^2=8(y-2)=8 y-16 \Rightarrow y^2-8 y+16=0 \quad \Rightarrow(y-4)^2=0 \Rightarrow y=4,4 }

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

\mathrm{\therefore \, \, x=4-2=2}, Thus the required point is \mathrm{(2,4)}.

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chirag

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