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the number of normals to a parabola y^2 = 8x through (2,1) is

the number of normals to a parabola y^2 = 8x through (2,1) is

Grade:11

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
6 years ago
Equation of normal
y = mx – 2am – am3 here a= 2 from parabola
​Passes through (2,1)
1= 2m – ​4m – ​2m​3
2m​3 ​+ 2m + 1 =0
Derivate of above function is 6m​2+ 2 which is always positive so thiswill be increasingfunction. So it will have only one root.
So onenormal.​

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