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Maths-

General

Easy

Question

Let the line $l x$ + my = 1 cut the parabola y² = 4ax in the points A and B. Normals at A and B meet at point C. Normal from C other than these two meet the parabola at D then the coordinate of D are

(a, 2a)
$(\frac{4 a m}{l^{2}}, \frac{4 a}{l})$
$(\frac{2 a m^{2}}{l^{2}}, \frac{2 a}{l})$
$(\frac{4 a m^{2}}{l^{2}}, \frac{4 a m}{l})$

The correct answer is: $open parentheses fraction numerator 4 a m to the power of 2 end exponent over denominator l to the power of 2 end exponent end fraction comma fraction numerator 4 a m over denominator l end fraction close parentheses$

Three points A, B and D are co-normal.
y² – 4a $open parentheses fraction numerator 1 minus m y over denominator l end fraction close parentheses$ = 0
y₁ + y = $fraction numerator negative 4 a m over denominator l end fraction$
$rightwards double arrow$ y₁ + y₂ + y₃ = 0
$rightwards double arrow$ y₁ = $fraction numerator 4 a m over denominator l end fraction$

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