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Friday, January 15, 2010

Q.85. Tangents to the parabola through the origin

Question 85.
Find the equations of the lines tangent to the parabola y = x^2 - 2x + 4 that go through the origin.

Answer 85.
Let y = mx be the tangents
Solving it with y = x^2 - 2x + 4
=> mx = x^2 - 2x + 4
=> x^2 - (m + 2)x + 4 = 0
For the line y = mx to be a tangent, discriminant of this quadratic should be zero
=> (m + 2)^2 - 16 = 0
=> m + 2 = - 4 or + 4
=> m = - 6 or 2
=> y = 2x or y = - 6x are the required tangents.

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