    Question

# A pair of tangents are drawn from a point on the directrix to a parabola y2=4ax. The angle formed by the tangents will always be 90∘

A

True

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B

False

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Solution

## The correct option is A True Let's draw a parabola first p is the point on the directrix and A and B are the points where tangents from P touches the parabola. Let P≡(−a,y), both tangents at A point is, The equation for tangent at A point is, ty=x+at2 for tangent at A t1y=−a+at21 y=at1(t21−1) ..............(1) for tangent at B t2y=−a+at22 y=at2(t22−1) ......(2) Eliminating y t1−1t1=t2−1t2 t1−t2=1t1−1t2 =t2−t1t1t2 i.e., t1t2=−1 We know slope of a tangent at a point given by parameter is (1t) If 2 tangent are perpendicular then product of slope will be -1. i.e., 1t1.1t2=−1 t1t2=−1 ∴ Tangent are at right angle to each other  Suggest Corrections  0      Similar questions  Related Videos   Chords and Pair of Tangents
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