10-seconds challenge-12

Geometry Level 3

If y = 2 x + c y=2x+c is tangent to parabola y 2 = 8 x y^{2}=8x .Then find the value of c c .


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The answer is 1.

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3 solutions

Rishabh Jain
Mar 15, 2016

Tangent of slope m m to parabola y 2 = 4 ( 2 ) x y^2=4(2)x is y = m x + 2 m y=mx +\dfrac{2}{m} . Tangent of slope 2 2 will be : y = 2 x + 1 y=2x+1 c = 1 \implies c=\boxed 1

Akhil Bansal
Mar 15, 2016

Equation of tangent on point ( x 1 , y 1 ) (\color{#3D99F6}{x_1},\color{#20A900}{y_1}) on parabola is y y 1 = 4 ( x + x 1 ) y\color{#20A900}{y_1} = 4(x+\color{#3D99F6}{x_1}) .
On comparing above equation with given equation of tangent , y = 2 x + c y = 2x + c , y 1 = 2 \Rightarrow \color{#20A900}{y_1} = 2 and x 1 = c / 2 \color{#3D99F6}{x_1} = c/2 .
Point ( x 1 , y 1 ) (\color{#3D99F6}{x_1},\color{#20A900}{y_1}) lies on given parabola,
4 = 8 ( c 2 ) c = 1 4 = 8\left( \dfrac{c}{2}\right) \Rightarrow c = 1


Moderator note:

Simple standard approach.

Its not a 10sec approach!

Md Zuhair - 3 years, 5 months ago

how to do it in 10 sec ? it took 16 sec. lol !

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