Question

48. The angle between the tangent drawn from the point (1, 4) to the parabola y2 = 4x is
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Answer 1

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=> (theta) = π/3

•We know that tangent to y² = 4ax is

y = mx + a/m.

=> tangent to y² = 4x is y = mx + 1/m

Since, tangent passes through (1,4)

4 = m + 1/m

=> m² - 4m + 1 = 0

m1 + me = 4

and m1m2 = 1

and |m1 - m2| = √(m1+M2)² - (4m1m2

= √12 = 2√3

Thus, the angle between tangent

tan(theta) = |(m2-m1) / (1 + m1m2) |

= | 2√3/1+1 |

=> (theta) = π/3

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Answer 2

Answer:

=> (theta) = π/3

•We know that tangent to y² = 4ax is

y = mx + a/m.

=> tangent to y² = 4x is y = mx + 1/m

Since, tangent passes through (1,4)

4 = m + 1/m

=> m² - 4m + 1 = 0

m1 + me = 4

and m1m2 = 1

and |m1 - m2| = √(m1+M2)² - (4m1m2

= √12 = 2√3

Thus, the angle between tangent

tan(theta) = |(m2-m1) / (1 + m1m2) |

= | 2√3/1+1 |

=> (theta) = π/3