stion-images/batch-001/3372fde0b237.webp" data-orsrc="https://uploads-pracbee-ramanuj.s3.ap-south-1.amazonaws.com/pyq-question-images/batch-001/3372fde0b237.webp" loading="lazy" style="max-width:100%;height:auto;display:block;margin:0 auto;max-height:40vh;vertical-align:baseline" alt="JEE Main 2024 (Online) 9th April Evening Shift Mathematics - Parabola Question 40 English Explanation">

$$\begin{aligned} & \text { For } D, y=2 a t_3 \\ & \Rightarrow x=a\left(t_1 t_3+t_2 t_3-t_1 t_2\right) \\ & C D=\left|a\left(t_1 t_3+t_2 t_3-t_1 t_3\right)-a t_3^2\right| \\ & A M=\left|2 a t_1-2 a t_3\right| \\ & B N=\left|2 a t_3-2 a t_2\right| \\ & \left(\frac{A M \cdot B N}{C D}\right)^2=\left(\frac{4 a^2\left(t_1-t_3\right)\left(t_3-t_2\right)}{a\left(t_1 t_3+t_2 t_3-t_1 t_3-t_3^2\right)}\right)^2 \\ & =\left(\frac{4 a^2\left(t_1-t_3\right)\left(t_3-t_2\right)}{a\left(t_1-t_3\right)\left(t_2-t_3\right)}\right)^2 \\ & =16 a^2=16 \cdot\left(\frac{3}{2}\right)^2=36 \end{aligned}$$

19:T4b3,

$$AB$$ का समीकरण

$$y\left(t_1+t_2\right)=2 x+2 a t_1 t_2$$

JEE Main 2024 (Online) 9th April Evening Shift Mathematics - Parabola Question 40 Hindi Explanation

$$\begin{aligned} & \text { D के लिए, } y=2 a t_3 \\ & \Rightarrow x=a\left(t_1 t_3+t_2 t_3-t_1 t_2\right) \\ & C D=\left|a\left(t_1 t_3+t_2 t_3-t_1 t_3\right)-a t_3^2\right| \\ & A M=\left|2 a t_1-2 a t_3\right| \\ & B N=\left|2 a t_3-2 a t_2\right| \\ & \left(\frac{A M \cdot B N}{C D}\right)^2=\left(\frac{4 a^2\left(t_1-t_3\right)\left(t_3-t_2\right)}{a\left(t_1 t_3+t_2 t_3-t_1 t_3-t_3^2\right)}\right)^2 \\ &

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