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Maths-

General

Easy

Question

Tangents are drawn from a point P to the parabola y² = 8x such that the slope of one tangent is twice the slope of other. The locus of P is

a circle
a straight line
a parabola
an ellipse

The correct answer is: a parabola

y² = 8x, a = 2 $rightwards double arrow$ 2y $fraction numerator d y over denominator d x end fraction equals 8$ $rightwards double arrow$ $fraction numerator d y over denominator d x end fraction equals fraction numerator 4 over denominator y end fraction$

m₁ = 2m₂ $rightwards double arrow$ 1/t₁ = 2t₂ … (i)
K = a(t₁ + t₂) = 2(t₁ + t₂) = 2(3t₁) $rightwards double arrow$ t₁ = K/6
$rightwards double arrow$ t₂ = K/3
Now, h = at₁t₂ $rightwards double arrow$ h = 2 . k/6 . k/3 $rightwards double arrow$ k² = 9h
Lows of P y² = 9x

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